Topology optimization for metal additive manufacturing: current trends, challenges, and future outlook

ABSTRACT

Metal additive manufacturing is gaining immense research attention. Some of these research efforts are associated with physics, statistical, or artificial intelligence-driven process modelling and optimisation, structure–property characterisation, structural design optimisation, or equipment enhancements for cost reduction and faster throughputs. In this review, the focus is drawn on the utilisation of topology optimisation for structural design in metal additive manufacturing. First, the symbiotic relationship between topology optimisation and metal additive manufacturing in aerospace, medical, automotive, and other industries is investigated. Second, support structure design by topology optimisation for thermal-based powder-bed processes is discussed. Third, the introduction of capabilities to limit manufacturing constraints and generate porous features in topology optimisation is examined. Fourth, emerging efforts to adopt artificial intelligence models are examined. Finally, some open-source and commercial software with capabilities for topology optimisation and metal additive manufacturing are explored. This study considers the challenges faced while providing perceptions on future research directions.

GRAPHICAL ABSTRACT

KEYWORDS:

• Metal additive manufacturing
• additive manufacturing
• topology optimisation
• aerospace
• automotive
• medical

1. Introduction

Metal Additive Manufacturing (MAM) has attracted increasing attention because it realises geometrically complex, fully functional metallic structures that are hard to produce by traditional processes (du Plessis et al. 2019; Fayazfar et al. 2018; Bacciaglia, Ceruti, and Liverani 2020; Plocher and Panesar 2019; Zhang et al. 2020a; Townsend et al. 2016; Bhavar et al. 2017; Blakey-Milner et al. 2021; Pan, Karnati, and Liou 2020b; DebRoy et al. 2018; Gisario et al. 2019; Lewandowski and Seifi 2016; Frazier 2014; Kok et al. 2018). Most traditional manufacturing methods limit topological design complexities of parts which are considerably feasible by Additive Manufacturing (AM) processes. Topology optimisation (TO) establishes the best material or structural layout with a predetermined design domain by optimising an objective parameter against one or a set of constraints. Due to this design freedom TO offers, organic shapes having intricately connected features are common. Although optimum designs are obtainable compared to other structural optimisation methods, TO was largely theoretical in the past because of limitations on manufacturing techniques to actualise such designs. This narrative is fast-changing, and in the last decade, there have been enormous efforts to consider TO in the design workflow of various components due to the advancement of AM processes. Classifications of popular TO and MAM methods are shown in Figure 1. To indulge the reader, there are several reviews on equipment-focused AM (Frazier 2014; Kok et al. 2018; Gisario et al. 2019), microstructure and mechanical properties of AM parts (Fayazfar et al. 2018; Bhavar et al. 2017; DebRoy et al. 2018; Frazier 2014; Gisario et al. 2019; Gu et al. 2012; Yap 2015; Bourell et al. 2017; Zhai, Lados, and LaGoy 2014; du Plessis, Yadroitsava, and Yadroitsev 2020; Kok et al. 2018; Lewandowski and Seifi 2016; Townsend et al. 2016), cost models (Gisario et al. 2019; Ahn 2016), and simulation of AM processes (Bandyopadhyay and Traxel 2018; Megahed et al. 2016; Gatsos et al. 2019; Srivastava et al. 2020a; Kouraytem et al. 2021; Bayat et al. 2021; Hashemi et al. 2021). Some TO-specific reviews can be seen in Wang et al. (2021c), Xia et al. (2016), van Dijk et al. (2013), Rozvany (2008), and Reddy et al. (2016a) while TO for AM is observed in Gao et al. (2015), Meng et al. (2019), Abdulaziz et al. (2020), Liu et al. (2018a), Blakey-Milner et al. (2021), and Plocher and Panesar (2019).

Figure 1. Summary of major topology optimisation and metal additive manufacturing techniques. Metal AM portion adapted from (Kok et al. 2018).

Although there are now a plethora of methods to topologically optimise structures, they can be categorised into 4 major methods as shown in Figure 1: density-based, evolutionary, boundary variation, and non-gradient-based methods. Density-based methods make use of pseudo-density variables as the optimisation’s design variables with limits placed on this parameter usually to establish material phases (e.g. solid, void, fluid., etc.). There are two popular density-based methods: Solid Isotropic Material with Penalisation (SIMP) and the Rational Approximation of Material Properties (RAMP) (Bendsøe et al. 2011; Toyserkani et al. 2021). These methods are defined by the material interpolation function, while SIMP uses a power-law function, RAMP utilises a rational function. The evolutionary methods enable the successive removal, in the case of ESO, or successive removal and addition, in the case of Bi-directional ESO (BESO), of material during the optimisation process. In the boundary variation methods, level and phase functions are used to identify solid, void, or boundary regions. In nascent times, non-gradient-based have been gaining some popularity especially because of the advancements of artificial intelligence models. Other non-gradient-based methods which have been used for topology optimisation as listed in Figure 1 are Genetic Algorithm (GA), Particle Swarm Optimisation (PSO), etc.

While Powder Bed Fusion (PBF), Direct Energy Deposition (DED), and Binder Jetting (BJ) form the most popular MAM technologies as pointed out by Toyserkani et al. (2021), in this study, most MAM technologies are first broadly classified as either powder-bed, directed energy deposition, or sheet lamination. MAM processes can also be identified or classified by their working mechanisms such as lasers, electron beams, optical systems, material delivery, etc. The classifications in Figure 1 are according to how the feedstock material is being consolidated. Within powder bed processes, Laser Fusion (LF) often called Laser Powder Bed Fusion (LPBF) and Electron Beam Melting (EBM) are popular fusion processes while Binder Jetting (BJ) is a unique metal powder bed process that requires a binder to consolidate powder particles to form a ‘green’ part which needs to be heat treated for binder removal and curing. For DED processes, feedstock materials are either powder-fed or wire-fed. While materials that are powder-fed cannot be consolidated by electron beams because vacuum conditions will be required, wire-fed materials can be worked upon by either lasers or electron beams. Direct Metal Deposition (DMD) and Electron Free-Form Fabrication (EF³) are popular laser and electron beam DED technologies respectively. In sheet lamination, thin sheets of metal are joined together in a solid-state manner usually by ultrasonic consolidation (Toyserkani et al. 2021). Sheet lamination can be beneficial because joining is done at much lower temperatures than the material’s melting temperature, consequently, the microstructure of the final part closely matches that of the parent material. However, there are limitations on compatible materials possible and design complexities.

AM’s flexibility makes it ideal for its integration with TO (Bendsøe and Kikuchi 1988; Bendsøe et al. 2011). However, TO results are not always AM-friendly (Liu et al. 2018b; Meng et al. 2019; Mirzendehdel and Suresh 2016), so it is critical to incorporate AM limitations into TO to fully improve the integration between design and fabrication in actual applications (Wu et al. 2018; Mhapsekar, McConaha, and Anand 2018; Zegard and Paulino 2016; Zhu et al. 2021b). To that purpose, great effort has been considered in the design stage to optimise support structures (Li et al. 2016a; Xiong et al. 2020; Zhou and Zhang 2019), reduce thermal accumulation (Allaire and Bogosel 2018; Wang and Qian 2020; Zhou, Liu, and Lin 2019a; Miki and Nishiwaki 2022), ease residual stress and deformation (Cheng and To 2019; Cheng et al. 2019a; Bartsch et al. 2019; Zhang et al. 2020a; Misiun et al. 2021; Allaire and Jakabčin 2018; Allaire, Bihr, and Bogosel 2020; Pellens et al. 2020), and so on.

This review focuses on the intervention of TO methods in MAM design workflow, especially within the technical research space. The review is targeted to address two broad scopes: industry applications of TO and MAM, and the use of TO within the Design for Additive Manufacturing (DfAM) framework considering metals. In the first scope, the extent to which the symbiosis between TO and MAM has assisted industry-specific design applications for improved functionalities, ease of manufacturability, and general freedom of design expression is discussed in Section 2. The second scope elaborates on the use of topology optimisation to fulfil aspects of the design for metal additive manufacturing framework. Under this scope, the role of TO in the design of support structures prevalent in thermal-based powder-bed processes is examined in Section 3. Thermal-based powder-bed technologies form the most utilised MAM and support structures are inevitable for most of them. As will be explained in this review, many research efforts have shown that TO can assist in generating optimal support structures while limiting material usage. Since MAM processes present manufacturability constraints, this review in Section 4, will examine the various TO algorithms that have captured design-based constraints, such as overhang elimination, cavity-filling, feature size limits, and process-based constraints such as residual stresses and deformation. Furthermore, an aspect of design for additive manufacturing (DfAM) that has gained popularity is lightweighting through porous structures. In Section 5, this review will explore the significance of TO in generating porous structures through latticing or infill strategies while recognising the considerations that should be made for MAM processes. In Section 6, the influence of nascent artificial intelligence models on the effectiveness and versatility of TO algorithms are discussed, and finally, some commercial and open-source software for TO and MAM are investigated in Section 7. A pertinent aspect of this review is the exploration of the status of these techniques and their effectiveness while identifying the inherent challenges and opportunities for future developments. Regarding the graphical abstract, the inner square shows the first scope of this study which reviews the adoption of TO and MAM in the industry covered in Section 2, while the outer circular ring reveals the second scope of TO and MAM within the DfAM framework which is covered from Sections 3 to 7.

2. Industry-related design and application

In simple terms, the entire purpose of design and manufacturing is to cater to individual or commercial market needs. While a variety of these needs are being addressed by several traditional and/or conventional manufacturing processes, AM has found immense application in some major industries. Developing metal parts through MAM poses unique design- and process-related challenges, unlike other polymer-based processes. TO has been a viable tool to address these challenges, although some of these algorithms are still in their infancy. In this section, the use of TO and MAM targeted for specific industrial purposes is studied.

2.1. Aerospace

Topology optimisation of structures related to aircrafts and spacecrafts will be considered under aerospace in this study. A review of TO applied in aircraft and aerospace structures was done by Zhu et al. (2021b). Although they briefly discussed the role AM could play in advancing structural designs, there was no elaborate discussion on MAM processes. However, an important conclusion they made is the fact that TO has been widely accepted for the design of aerospace structures, although with several manufacturability concerns. To investigate the symbiosis between TO and MAM within the aerospace industry, this study looks at several efforts within the past decade with some of these efforts shown in Figure 2. To demonstrate this, Süß et al. (2016) topologically optimised the main gearbox of a helicopter and adopted EBM (Ti-6Al-4V – material) as the chosen AM process. Three major objectives were targeted: weight savings, part consolidation, and the satisfaction of requirements for mechanical properties such as tensile, yield, and fatigue strength. Two optimisation solutions were obtained using different initial design domains, and separate redesigning strategies were utilised to reconstruct the topologies. One striking challenge was the intricacy and time spent reconstructing the topologies. Nonetheless, they achieved over 40% material reduction after reconstruction in both optimisation cases in addition to other objectives they accomplished. Seabra et al. (2016) leveraged TO and LPBF to design and manufacture a lightweight aircraft bracket shown in Figure 2(a) while maintaining functional stress levels. The general workflow is similar to (Süß et al. 2016); however, parts produced by LPBF are more prone to porosities and residual stresses compared to EBM if optimum process parameter selections are not made; therefore they performed Hot Isostatic Pressing (HIP) after printing. A 28% reduction in weight was achieved even though the bracket’s material was changed to a Titanium alloy from an aluminum alloy. Another application is observed in Magerramova, Vasilyev, and Kinzburskiy (2016), where turbine blades were designed by a TO formulation consisting of a strain energy minimisation as the objective function and two constraints: a double reduction in material volume (from the original design domain) and a limit on the first 6 eigenfrequencies. Constraining the eigenfrequencies is necessary to detune the resonance frequency in the design of low-pressure turbines (LPT). It should be noted that due to the tomography of turbine blades, there could be very thin features in the design that will pose a manufacturing challenge. To circumvent this challenge, a minimum feature thickness of 0.15 mm was imposed during the design. Representative small-sized blades were printed using a Nickel-based superalloy via LPBF. The popular GE Aircraft Engine bracket was redesigned and manufactured by Direct Metal Laser Sintering (DMLS) in López-Castro et al. (2017) as shown in Figure 2(b). The aim was to reduce the weight of previous versions of this bracket by printing an optimised alternative using Stainless Steel AISI 15-5PH as opposed to Ti-6Al-4V. To adhere to geometric constraints for the AM process, a minimum feature size limit of 9 mm was placed during TO, and a 56% reduction in weight was realised while keeping close functional stress and deformation profiles with the original design. Other areas that explored the use of TO and MAM for metal aircraft components without exploring manufacturability can be seen in the aircraft landing gear and engine mount in Munk et al. (2019), tesla valve in Gaymann, Montomoli, and Pietropaoli (2017), and aircraft brackets in Gebisa and Lemu (2017a) and Fetisov and Maksimov (2018).

Figure 2. The application of TO and MAM in the development of aircraft brackets as developed by (a) (Seabra et al. 2016). Reproduced with permission from Ref. (Seabra et al. 2016). Copyright 2016, Elsevier, and (b) (López-Castro et al. 2017). Reproduced with permission from Ref. (López-Castro et al. 2017). Copyright 2017, Elsevier.

For space-related applications, the design of mirrors using TO and MAM was explored by Herzog et al. (2015). Mirrors find a useful application in spaceflight, therefore, there were critical properties required, such as good structural rigidity, quality surface finish, and the ability to withstand severe vibrational effects. In light of this, an initial CAD file placed under appropriate load and boundary conditions was optimised for stiffness maximisation and placed under a material volume and a 250 Hz natural frequency constraint. The mirror was printed using two MAM processes: EBM with Ti-6Al-4V and DMLS with AlSi10Mg. Due to the unique specifications required by the mirror, several post-processing steps were taken such as HIP to reduce porosity, and preliminary machining with a mill for resurfacing, grinding and polishing. The last two processes are important phases in general optical fabrication. Although the mirrors printed successfully using both materials, the aluminum mirror was more successful with fewer porosities and a better micro roughness. Another space mirror was developed by Hu et al. (2017) by topology and sizing optimisation. No manufacturability study was performed; however, extrusion (Ishii and Aomura 2004; Zhou et al. 2002), and void filling (Liu et al. 2015) constraints were included in the TO step. . Orme et al. (2017) designed and manufactured a mock framework (consisting of 4 legs and a hub) of a lunar spacecraft. As seen in Figure 2(c), a design domain (in grey) was obtained and optimised for minimal mass while limiting the natural frequency and stress to >60 Hz and <115 MPa respectively. The optimised framework was printed using an EOS M290 using AlSi10Mg as material and due to the framework’s size relative to the machine, it was designed to have 4 identical legs. Due to the limitations of the optimisation software used, CAD interpretation of the optimised topology was necessary for post-optimisation FEA, support minimisation, and overall printability.

A critical aspect of the aerospace industry is certification and standardisation of air/space-crafts and important components such as engines/engine parts, and structural frameworks which, oftentimes, take time. Without certification and standardisation, these components are prone to failure leading to catastrophic events and losses. The United States Federal Aviation Administration mentioned that they spent 5 years certifying the Boeing 737 MAX between 2012 and 2017 (Airworthiness Certification 2022). Most of the aerospace-related efforts reviewed in this study are within the last 6 years with little to no mention of the homologation process for the designed or redesigned components. The reason could be that these new designs are still more theoretical than practical as further experimental studies need to be done to certify their performances. A study that considered part qualification is the work done by Willner et al. (2020). For spacecraft components, a technology readiness level (TRL) of 7 is required for the final system test, launch, and operations. In Willner et al. (2020), it was opined that their topologically optimised and additively manufactured spacecraft bracket was eligible for TRL 3 as is, with a qualification process increasing this level to TRL 5. However, to raise this certification level to TRL 7, testing of the assembled system including the bracket needed to be done. This action was beyond the scope of their study and therefore limited the homologation process. Singamneni et al. (2019) stated that the certification and standardisation of AM parts is the most difficult stage for the aircraft industry due to several limitations which can be summarised as the current evolution of the manufacturing technology. Since most MAM technologies are still evolving, obtaining widely acceptable standards for AM materials, processes, quality control, and assessment, and design is still lacking. This is a key contributing factor that hinders the homologation of the many newly designed aerospace components. This hindrance is further exacerbated by the cost and length of time for these certification and standardisation procedures.

2.2. Medical

Over the past decade, the need and relevance of AM for medical purposes have greatly increased. For example, in 2011 in Belgium, Dr. Jules Poukens and his team implanted the world’s first additively manufactured mandible in a patient (Xillo 2011). The achievement of this milestone is significant in many ways because it has revealed opportunities in the design and manufacture of medical implants (Leary 2018), such as patient-tailored implants (Shidid et al. 2016) or lattice-based implants with mechanical and geometric properties closely similar to the host’s bone (Wang et al. 2016; Reinhart and Teufelhart 2011). Other than lattice structure design, one popular approach in designing patient-tailored implants is through TO or a combination of TO and lattice structures which will be the focus of this section. In the design of implant devices and bone tissue engineering (Bose, Vahabzadeh, and Bandyopadhyay 2013; Wang et al. 2016), bone remodelling is a core aspect that involves the adaptation of the bone’s internal structure to adequately support external loading conditions. To achieve this, the principal stress paths of the implant’s structure have to be optimally re-organized to maximise structural rigidity (Goda et al. 2019). Additionally, an undesirable phenomenon that occurs in an inappropriately matched bone-implant assembly is stress shielding where a much stiffer implant compared to its neighbouring bone region results in inaccurate bone remodelling (Haase and Rouhi 2013; Park, Lee, and Sutradhar 2019). Several efforts have employed TO and MAM to address these aspects.

Al-Tamimi et al. (2019) studied the re-design of metallic bone plates in the treatment of bone fractures. To combat stress shielding, the plates were topologically optimised to obtain an equivalent stiffness comparable to that of a cortical bone. The optimised plates were printed via EBM using Ti6Al4V and several characterisations were done to observe their tensile, hardness, and surface roughness properties. The results of tensile tests revealed close matches to numerical results. In-vitro testing of the plates was done to understand the speed and quality of biological bonding with surrounding tissue, and it was found that rough surfaces of the EBM plates contributed to better bonding compared to smoother commercially produced plates. Contrary to previous related studies, they concluded that rougher EBM plates without any post-processing contributed to higher cell binding and proliferation. In a similar vein, He et al. (2018) combated stress-shielding in LPBF-manufactured Ti6Al4 V hip prosthesis through a combination of TO and lattice design. Although no in-vitro biological testing was done, it was noticed that the stress shielding increase (SSI) (Weinans et al. 2000; Fraldi et al. 2010) was reduced by over 50% in the optimised design and could last longer than 10⁷ life cycles compared to the generic implant. Some bottlenecks identified in this study are the absence of the influence of the bone-implant interface which often results in aseptic loosening and the a priori approach taken to obtain the unit cell type and size for lattice structures.

To design a patient-tailored mandibular implant, Cheng et al. (2019b) developed a Titanium implant through a 3D reconstruction of the patient’s defective mandibular and TO. Two broad functionalities were considered: aesthetics and functionality. For functionality, four objectives were specified: fixation, support, bone ingrowth, and chewing. After TO, micro-pores were introduced to inhibit stress-shielding and encourage bone ingrowth. The implant was printed via LPBF using Ti6Al4V, but neither mechanical nor in-vitro testing was done. A multi-objective TO model to optimise stiffness under various functional routines was utilised to design a pelvic implant by Iqbal et al. (2019). This design strategy was fulfilled for four initial design domains obtained from different resection types as observed in Figure 3. The implant was printed using EBM in Ti6Al4V and was implanted in a patient in China. Some challenges and assumptions were the adoption of less realistic static loading conditions, the exclusion of the effects of connecting muscles and ligaments, and performance evaluation based on numerical analysis only without experimental mechanical test validations. For future developments, the numerical model can be strengthened by using dynamic loading inputs which will more closely match the natural physiological routine.

Figure 3. Topology-optimised prostheses for four resection types. Reproduced with permission from Ref. (Iqbal et al. 2019). Copyright 2019, Elsevier.

In this paragraph, three major TO approaches for implant designs are summarised. While the general formulation and implementation of TO can be found here (Andreassen et al. 2011; Ibhadode et al. 2021),

1. The first popular approach is the use of a multi-objective functional, usually compliance or strain energy (Iqbal et al. 2019; Guo and Yin 2019; Liu, Jiang, and Lin 2020b; Jiang et al. 2017). Here, since the daily routine of the physiological region exerts several load types on the implant’s structure, a consolidated compliance function is expressed as the summation of the weighted individual load compliances. Consolidation is facilitated by introducing weight factors associated with the compliances where the value of a weight factor depends on the priority given to the functional load.

2. A second approach is stress-based TO. Instead of going with a multi-objective function, global compliance resulting from the summed effects of the loads is maintained as the objective while a stress constraint is imposed to limit the structure’s failure (Al-Ali et al. 2017; Deaton and Grandhi 2016).

3. In the third approach, infill and perimeter TO frameworks are developed to generate structures that nearly model the venous or porous nature of bone structures (Wu et al. 2018; Zhao and Zhang 2021a, 2021b; Park et al. 2018). This involves the addition of one or more constraints that control the distribution of the pseudo-density field during optimisation. The applications of TO and MAM in medicine can mainly be seen in the development of implants and prostheses for mandibles, craniums and facials, hips, dental implants, and spines as shown in Figure 4.

Figure 4. Major applications of TO and MAM in medicine: mandibles (reproduced with permission from Ref. (Li et al. 2020a). Copyright 2020, Elsevier), cranium and facial (Park et al. 2021), pelvic and hip (reproduced with permission from Ref. (Iqbal et al. 2019). Copyright 2019, Elsevier), dental (reproduced with permission from Ref. (Park et al. 2019). Copyright 2019, Elsevier), and spine (reproduced with permission from Ref. (Wang et al. 2020a). Copyright 2020, Elsevier).

There are several other non-metallic additively manufactured implant designs developed in the past years (Park, Lee, and Sutradhar 2019; Jiang et al. 2017; Živčák et al. 2018; Gómez Pérez, Medellín-Castillo, and Espinosa-Castañeda 2017; Sutradhar et al. 2015, 2010; Moussa et al. 2020; Hu et al. 2019; Li, Wu, and Lin 2020a).

2.3. Automotive

In a bid to push up the efficiencies of modern automobiles, several advanced techniques such as turbocharging, advanced spark ignitions, better emission control, fuel consumption, advanced braking, steering and suspension systems, etc. have been devised. To achieve these technologies, ingenious design and manufacturing techniques must be adopted. Several research efforts are beginning to introduce TO and additive manufacturing into the design workflows for these automobile components and systems. It is particularly observed that many case studies focus on parts in and around the suspension/wheel system and engine. In Dalpadulo, Pini, and Leali (2020a), Walton and Moztarzadeh (2017), Vaverka, Koutny, and Palousek (2019), Reddy et al. (2016b), and Bikas et al. (2016a), wheel knuckles or uprights for Formula race cars were studied. While Bikas et al. (2016a), Dalpadulo, Pini, and Leali (2020a), and Vaverka, Koutny, and Palousek (2019) printed topology-optimised samples using AlSi10Mg by LPBF, Walton and Moztarzadeh (2017) and Reddy et al. (2016b) printed optimised samples using Ti6Al4V by EBM and LPBF respectively. In all the listed studies, significant weight savings were attained while maintaining decent performances, however, in Walton’s study, the cost of EBM against the machined alternative was over 700%. Since the manufacturing costs for EBM or LPBF parts are still comparatively high, it is pertinent that these manufacturing methods are reserved for high-priority or sensitive parts where performance is given higher consideration than cost. Moreover, although most thermal-based MAM processes are meant for low-volume or customised productions, it is highly recommended that more studies investigate the cost of MAM in comparison with alternative production processes. Dalpadulo, Pini, and Leali (2020a) went further to explore several workflows for part simulation, print preparation, and process simulation in Catia’s 3DExperience. For efforts that compare MAM to other manufacturing processes, Großmann et al. (2020) compared a topologically optimised riveting tool printed via LPBF to an optimised version constrained for milling and an original milled. Amongst others, their weights, manufacturing costs, time, simulated maximum displacements, equivalent stresses, and waste material were compared. The optimised MAM part outperformed the others in weight, waste material, and equivalent stress; however, it performed less in manufacturing time and cost. With research and development, it is expected that time and cost for MAM parts will be reduced; however, relatively simple parts such as the riveting tool might be easier and cost-effective to manufacture using traditional processes. Furthermore, as mentioned previously, if the part is not meant for high performance or safety such that precise functional requirements over production costs are justified, non-thermal-based MAM such as Binderjetting (BJ), material extrusion, or traditional production processes are recommended.

Tyflopoulos, Lien, and Steinert (2021) redesigned the front and back brake callipers that were printed using Ti6V4Al by LPBF in Figure 5(a) while Bici, Broggiato, and Campana (2016) topologically optimised a suspension wishbone attachment without printing it although they opined that it was a good candidate for MAM. Junk, Fleig, and Fink (2017) redesigned a brake mount through TO and prototyped it via BJ. After refinements and smoothing, the final part was printed via LPBF using AlSi10Mg. An interesting aspect was the relationship established between the weight reduction in the brake mount and the carbon footprint. It was estimated that an 81 g reduction in the mass could lead to a reduction of 855 mg/100 km of CO₂; Barbieri et al. (2018) proposed that steel pistons could be adopted in place of their contemporary aluminum counterparts because they can take more mechanical and thermal loads. Steel pistons were redesigned by TO resulting in a 9% increase in weight, further design studies were recommended to ensure the redesigned pistons meet the functional requirements. Unfortunately, neither manufacturability nor experimental mechanical tests were done to validate the design solution. Other applications of TO and MAM can be seen in the gearbox housing redesign by Barreiro et al. (2019) printed using AlSi10Mg by LPBF, race-car upright design by Hunar et al. (2020) in Figure 5(b), diesel engine support by Marchesi et al. (2015) in Figure 5(c), steering column support by Mantovani, Campo, and Ferrari (2020), and automotive fixtures by Naik et al. (2019); they are all summarised in Table S1.

Figure 5. Applications of TO and MAM in the automotive industry: (a) brake calliper (Tyflopoulos et al. 2021), (b) upright design (Hunar et al. 2020), (c) diesel engine support (Marchesi et al. 2015).

2.4. Others

Several other industries have benefited from the symbiotic relationship enjoyed by TO and MAM although not as much as the industries listed above. As far back as 2007, Ngim reported the design of axisymmetric components using a material minimisation, stress-constrained TO process (Ngim, Liu, and Soar 2007). The design strategy was reported to be suitable for a range of components such as brake disks, flywheels, pressure vessels, etc. Although a prototype was printed of the optimised design using a nylon material via SLS, it was reported that metallic materials could be used as they will have properties similar to carbon steel which was used during the simulation. Herbin, Grzesiak, and Krolikowski (2017) considered a 7-Degree of Freedom ExoArm for lightweighting since the weight of the components of the ExoArm impacts the power on the drives. First, the original material specification Ti-6Al-4V was replaced with 7075 aluminum and steel for weight reduction. Next, TO and lattice structures were applied to further reduce the weights of the ExoArm clamps. The clamps were printed using LPBF achieving a material reduction of 45% and above for all parts optimised. TO and MAM have also been explored in the construction industry. Huang, Deng, and Lam (2021) investigated the performance of additively manufactured topology-optimised tubular joints with their hollow square-section welded counterparts. Several mechanical tests were performed, and some important conclusions drawn are: a 1.6% difference in the Young’s Modulus between the printed and welded tubular joints, the printed joints gave more symmetric stress distributions compared to the welded joints, the maximum stress was decreased by 49% when TO was utilised to design the printed parts. Using TO, Lynch et al. (2013) proposed some guidelines for the design and optimisation of parts to be manufactured by cold-spray AM. The design guidelines include the consideration of planar features, smooth transition between surfaces for continuous spraying, deposition angle and cross-sectional geometry, feature thickness limitations based on cold spray parameters, etc. Wu et al. (2017) worked on the redesign of a plastic injection tool using a thermo-mechanical TO model and lattices. Steuben et al. (2017) investigated the redesign of an unmanned underwater vessel by a meta-material TO model with acoustic tunability. Other applications can be found in Figure 6 and Table S1 in the supplementary file.

Figure 6. Application of TO and MAM in other industries (a) redesign of a welding jig (reproduced with permission from Ref. (Schuh et al. 2020). Copyright 2020, Elsevier) design of a phase change material-based heat sink (reproduced with permission from Ref. (Ho et al. 2021). Copyright 2021, Elsevier).

2.5. Sustainability

In the aerospace and automotive industries, strict requirements on the final part quality are usual. Often, the application of TO and MAM can produce lightweight parts that meet certain operational requirements such as structural rigidity. However, there are other precise specifications required by these industries in terms of surface finishes, tolerances, etc., which might be difficult to attain by MAM only. It is, therefore, important to understand how MAM compares to conventional manufacturing or machining in terms of cost and energy demands especially when attempts are made to ensure a part meets up with these additional requirements. Furthermore, in light of this study, the influence of TO to contribute to more sustainable additively manufactured parts is important to point out. In Priarone et al. (2017), the cost and energy demand of a hybrid process of EBM and finish machining (FM) are compared to conventional machining (CM). As illustrated in Figure 7, the study showed that when an initial part is lightweighted by 25% (part 2) or 75% (part 3), the cost and energy required to produce the parts by CM increases slightly and this might be attributed to the resulting structural complexities compared to the original part. It is expected that this cost increase will become significant with much greater structural complexities. However, with EBM+FM, the cost of producing part 3, which is 75% lighter and more complex than part 1, is reduced by over 60% while the energy input required is reduced by over 50%. Although the cost of producing all parts using EBM+FM is considerably larger than that used by CM, TO plays a great role in ensuring MAM parts are not only optimally functional but more sustainable because of its lightweighting ability. Moreover, it is observed that energy demands by EBM+FM become less than CM for part 3. It is important to add that in Priarone et al. (2017), the additional cost and energy demand from FM were marginal compared to the overall demand by the hybrid process. In addition to MAM’s material reusability, MAM minimises energy and cost consumption substantially compared to CM when the part is designed with optimum material usage regardless of structural complexity. Note that the breakdown of the cost and energy components in Figure 7 is not shown, please refer to Priarone et al. (2017) for this. In a similar study, Tang, Mak, and Zhao (2016) estimated a 58% decrease in CO₂ emissions when binderjetting (BJ) was used to produce an optimised aerospace bracket compared to a computer numerically controlled (CNC) designed and produced bracket.

Figure 7. Cost and energy estimations for producing three parts using conventional machining (CM) and a hybrid electron beam melting (EBM) and finish machining (FM). Adopted from (Priarone et al. 2017).

In a study by Donofrio (2016), it was mentioned that 3D-printed topologically optimised structural steel joints developed by Arup had the potential to reduce transportation and storage costs compared to the original bulkier versions as the optimised structures were smaller and lighter. Studies by Munk and Miller (2022) and Gebisa and Lemu (2017b) also show that TO and MAM contribute to improving the product supply chain and minimising cost and environmental impact within several industries.

2.6. Remarks

TO has been extensively utilised in the design of parts for MAM, especially in the aerospace, medical, and automotive industries, however, it is observed that compared to the automobile industry, a wider range of applications has been considered in aviation and medicine.

In Table S1 in the supplementary file, 103 case studies on the application of TO and MAM in major industries drawn from several research efforts are presented. 29 of these case studies are categorised under aerospace (Süß et al. 2016; Seabra et al. 2016; Magerramova, Vasilyev, and Kinzburskiy 2016; López-Castro et al. 2017; Munk et al. 2019; Gaymann, Montomoli, and Pietropaoli 2017; Gebisa and Lemu 2017a; Fetisov and Maksimov 2018; Herzog et al. 2015; Orme et al. 2017; Willner et al. 2020; Song et al. 2021; Smith et al. 2016; Senck et al. 2020; Saudan et al. 2018; Muir et al. 2013; Li et al. 2016c; Ferro et al. 2017; Ferro et al. 2016; Faskhutdinov et al. 2017; Dagkolu, Gokdag, and Yilmaz 2021; Cucinotta, Raffaele, and Salmeri 2019; Galvao et al. 2021; Hu et al. 2017; Fan et al. 2021; Suárez et al. 2022; Chen et al. 2021b; Caivano et al. 2022; Leary et al. 2021; Berrocal et al. 2019), 25 under medical (Wu et al. 2018; Park, Lee, and Sutradhar 2019; Al-Tamimi et al. 2019; Cheng et al. 2019b; Iqbal et al. 2019; Gómez Pérez, Medellín-Castillo, and Espinosa-Castañeda 2017; Sutradhar et al. 2015; Moussa et al. 2020; Min et al. 2017; Deng et al. 2015; Bergmann et al. 2016; Li, Wu, and Lin 2020a; Liu et al. 2017; Carnicero et al. 2021; Kang et al. 2012; Lang et al. 2021; Bittredge et al. 2022; Liu et al. 2021b; Seebach et al. 2020; Seebach et al. 2017; Dai et al. 2018; Liu, Jiang, and Lin 2020b; Al-Tamimi et al. 2017; Al-Tamimi, Peach, and Bartolo 2018; Wang et al. 2020a; Lin et al. 2021), 25 under automotive (Dalpadulo, Pini, and Leali 2020a; Walton and Moztarzadeh 2017; Vaverka, Koutny, and Palousek 2019; Reddy et al. 2016b; Bikas et al. 2016a; Großmann et al. 2020; Tyflopoulos, Lien, and Steinert 2021; Bici, Broggiato, and Campana 2016; Junk, Fleig, and Fink 2017; Barbieri et al. 2017; Barbieri et al. 2018; Barreiro et al. 2019; Hunar et al. 2020; Marchesi et al. 2015; Mantovani, Campo, and Ferrari 2020; Mesicek et al. 2021; Ahn et al. 2021; Bujny et al. 2021; Cecchel 2020; DeBoer et al. 2021; Dalpadulo, Pini, and Leali 2021c; Dalpadulo, Pini, and Leali 2021a; Dalpadulo, Pini, and Leali 2021b; Abdi, Ashcroft, and Wildman 2018), and 23 under others (Ngim, Liu, and Soar 2007; Herbin, Grzesiak, and Krolikowski 2017; Lynch et al. 2013; Steuben et al. 2017; Ye et al. 2021; McEwen et al. 2018; Dalpadulo et al. 2020b; Nourbakhsh et al. 2016; Xiao et al. 2018; Xu et al. 2017; Pilagatti et al. 2021; See et al. 2022; Ueno et al. 2021; Alexandersen, Sigmund, and Aage 2016; Alexandersen et al. 2018; Dede, Joshi, and Zhou 2015; Hayes and Whiting 2021; Kanyilmaz et al. 2020; Mirzendehdel, Behandish, and Nelaturi 2022; Yan et al. 2022; Raz, Chval, and Stepanek 2022; Schuh et al. 2020; Ho et al. 2021). The major areas identified in these studies are the adopted TO model, optimisation objective, material, and MAM process. In Figure 8(a), the gradient-based density methods (SIMP, RAMP) are the most utilised and this is not far-fetched from the understanding that several current TO software tools are based on these methods. It is important to note that some non-gradient methods are gaining popularity, taking 10% of the total, in contrast to the comparatively more established evolutionary and level-set methods. Volume and compliance minimisation are equally popular as optimisation objectives in Figure 8(b). For material usage, 43% of the case studies use Ti6Al4V and other Ti-alloys in Figure 8(c) and although it takes the largest portion overall, Figure 8(e) reveals that the popularity of Ti-alloys is localised to the medical industry while there is a more even distribution of the usage of Ti-alloys, Al-alloys and Steel alloys in the aerospace and automotive industries. LPBF is the most used MAM process across all industries in Figure 8(d) and within the various specific industries in Figure 8(f). The BJAM process requires no support structures and typically performs better with geometrically simpler and bulkier shapes compared to LPBF, DMLS/SLS, and EBM. Considering the intricate results produced by TO, it is no surprise that it is the least used MAM process as observed in Figure 8(d,f). It should be stated that powder-fed processes received no attention in the case studies investigated. This is also no surprise because they require much simpler structural designs to be applicable; therefore, the rest of this study focuses on powder-bed processes.

Figure 8. Chart organisation of (a) topology optimisation models, (b) optimisation objectives, (c,e) materials, and (d,f) MAM processes across the aerospace, medical, automotive, and other industries.

In most case studies, the integration of AM constraints within TO is either not done or not reported. While only a few works (Orme et al. 2017; Mantovani, Campo, and Ferrari 2020) consider minimum feature size, overhangs, and build orientation optimisation during the design phase, a much larger portion of studies do not account for any MAM-related constraints which are widely developed in TO-AM research studies. Furthermore, void limitation/elimination is not observed to be implemented in any study. These constraints are developed to enable a more seamless and efficient design for manufacturability workflow. However, their lack of use might be attributed to either their absence or limited effectiveness within many commercially available TO software, designers do not consider them critical during the design process, or something else. A study on this dichotomy is important to understand the reasons for it and ways to ensure painstakingly developed TO-AM constraints are beneficial to designers during the DfAM process.

With the benefits of TO, it is expected that MAM will be widely adopted in more industries when two significant challenges are addressed: the high cost of MAM technologies (especially laser and electron beam techs, both initial and running costs) and limited build volumes and speed. Fortunately, Barnes (2021a), Barnes (2021b) showed that these challenges are being addressed with the introduction of multi-laser PBF systems. They showed that moving from a medium build volume single laser system to a large build volume quad laser system, production rates of a control arm increased by almost 100% while costs were reduced by almost 50%.

For many of the case studies amongst the major industries investigated and others, experimental validation studies for functionality are limited. It is important to benchmark the performance of candidate parts suitable for MAM based on functionality in addition to cost and manufacturability. Common functionalities such as stiffness/strength, frequency, heat transfer, pressure drop, surface roughness, etc., depending on the application, should be investigated, and evaluated against the performances of their counterpart designs made from traditional manufacturing processes.

3. Support structure design

AM components often require temporary support material to avoid collapse or warping during fabrication (Zhang, Yang, and Zhao 2020b; Blakey-Milner et al. 2021; Liu et al. 2018b; Mirzendehdel and Suresh 2016; Hussein et al. 2013; Strano et al. 2012; Calignano 2014; Hu, Jin, and Wang 2015; Langelaar 2016a; Cacace, Cristiani, and Rocchi 2017; Jiang, Xu, and Stringer 2018; Leary et al. 2019; Han et al. 2018). No matter how these support materials are removed chemically or mechanically, the use of sacrificial material increases total material usage, build time, and clean-up cost. For example, the largest portion of the cost for MAM, besides the equipment cost that is amortised, is the material cost of about 18% (Thomas and Gilbert 2014). Besides, the cost of support structure removal can make up for about 8% of the total product cost (Thomas and Gilbert 2014). Furthermore, research on support structures for MAM is important because support structures play a critical role in MAM by eliminating cracks, curls, sags, or shrinkages (Jiang, Xu, and Stringer 2018; Leary et al. 2019; Han et al. 2018). For example, in PBF, a high-power laser/electron beam selectively scans over metal powder to form a solidified metal layer to form parts layer-by-layer. PBF is known to contribute to residual stresses, distortion, and heat accumulation issues, which are due to the thermal stresses induced by the high and rapid heat input. To reduce these problems, PBF parts are commonly printed with support structures that are suitably designed to hold overhanging features, dissipate heat to prevent overheating, and anchor the parts to the substrate to reduce unwanted distortions and residual stresses (Mezzadri, Bouriakov, and Qian 2018; Zhou, Liu, and Lin 2019a; Cheng et al. 2019a; Bartsch et al. 2019; Zhang et al. 2020a).

For the reasons stated previously, support structure optimisation and minimisation are of significant interest within the AM community. Many researchers have used DfAM to optimise the design for the best manufacturing quality, minimising material for support structures and post-processing requirements (Thomas and Gilbert 2014; Blakey-Milner et al. 2021). As one of the most important DfAM tools, TO has been widely used due to its extensibility and attainability in optimising material distribution in a structure (Liu et al. 2018b; Meng et al. 2019; Mirzendehdel and Suresh 2016; Zhu et al. 2021b; Wang et al. 2016; Gardan and Schneider 2015; Zegard and Paulino 2016).

However, TO results are usually not AM-friendly (Liu et al. 2018b; Meng et al. 2019; Mirzendehdel and Suresh 2016), so it is critical to incorporate AM limitations into TO to improve this integration between design and fabrication in actual applications (Mhapsekar, McConaha, and Anand 2018; Zhu et al. 2021b; Zegard and Paulino 2016). To that end, great effort has been put in the design stage to eliminate enclosed voids and support structures (Li et al. 2016a; Xiong et al. 2020; Zhou and Zhang 2019), reduce thermal accumulation (Allaire and Bogosel 2018; Wang and Qian 2020; Zhou et al. 2019a; Miki and Nishiwaki 2022), ease residual stress and deformation (Cheng and To 2019; Cheng et al. 2019a; Bartsch et al. 2019; Zhang et al. 2020a; Misiun et al. 2021; Allaire and Jakabčin 2018; Allaire et al. 2020; Pellens et al. 2020), and so on. Among these constraints, designing structures and/or support structures with overhang angle control is considered an important AM constraint needed in TO and has drawn increasing attention to reduce the amount of support material usage and avoid printing failures (Mirzendehdel and Suresh 2016; Li et al. 2016a; Xiong et al. 2020; Strano et al. 2012; Gaynor and Guest 2016; van de Ven et al. 2020) or even get support-free structures (Zhou and Zhang 2019; Mezzadri et al. 2018; Guo et al. 2017; Langelaar 2018; Liu and To 2017; Zeng et al. 2015; Allaire et al. 2004; Liu and Yu 2020).

Besides support structures’ elimination, another related aspect is to design them for other loading conditions other than their weight, e.g. thermal loads or residual-stress-induced loads. Even though eliminating support material is beneficial and necessary, support structures are usually required in MAM, e.g. powder bed fusion (PBF) technique (Hussein et al. 2013; Strano et al. 2012; Jiang et al. 2018; Zeng et al. 2015). The functionalities of support structures, such as heat dissipation and part anchoring to counter residual stress and distortion, should not be ignored. The inclusion of support structures may alleviate the locally accumulated heat, as the underlying powder (e.g. powder bed fusion) does not conduct sufficient heat away, thereby reducing the possibility for residual stress and warping (Blakey-Milner et al. 2021).

The design of an effective support structure relies on its ability to contribute to print success without any support-related in-process errors while utilising the least amount of powder to produce those supports. Amongst all the design techniques, TO is one of the most important due to its versatility and ability to generate conceptual designs (Rozvany 2008; Bendsøe and Kikuchi 1988; Bendsøe et al. 2011; Meng et al. 2019; Liu et al. 2018b; Zegard and Paulino 2016; Zhu et al. 2021b; Allaire et al. 2020; Wang et al. 2021b; Kuo and Cheng 2019; Allaire et al. 2017; Zhou et al. 2016). Thus, researchers have been using TO to either design optimum support structures for AM or eliminate them as much as possible. Based on the different loading conditions, the optimisation of support structures can be classified into 3 categories: support structure for gravity load, thermal load, and residual-stress-induced load.

3.1. Support structure for gravity load

The primary role of support structures in AM is to support overhanging areas against gravity loads. In Figure 9, five types of support structures are shown: vertical strut-type, honeycomb, porous-type, contact-free, and topology-optimised supports. These temporary supports ensure a component does not collapse or warp during fabrication (Blakey-Milner et al. 2021; Liu et al. 2018b; Jiang et al. 2018; Leary et al. 2019; Han et al. 2018; Vouga et al. 2012).

Figure 9. Types of support structures under overhang areas in different parts. (a) vertical strut-type supports (b) honeycomb supports (Zhang et al. 2020a) (c) porous-type support (obtained with permission from GE Additive) (d) contact-free support (Cooper et al. 2017) (e) topology-optimised support (Langelaar 2019).

3.1.1. Support minimisation and optimisation

The importance of support structures for thermal-based MAM technologies has been elaborated on in the previous section. Notwithstanding, if support structures are not optimised or minimised, they can significantly increase build time, material, cost, removal time, and energy. Over the past years, many studies have implemented overhang elimination or self-supporting algorithms to ensure parts to be printed utilise minimal support structures. While several of these methodologies are elaborated in Section 4.1, some works that minimise and/or optimise support structures considering gravity loads are highlighted here. Pandey et al. (2004) proposed a weighted-averaging multi-criteria genetic algorithm to minimise support structure and build time while improving surface quality. Calignano (2014) investigated the manufacturability and geometrical precision of LPBF structures. The objective was achieved in two steps: first, understanding the limitation of construction without support structures, and second, optimising support structures by using experimental-driven statistical design (Taguchi L₃₆ design). A complex structure can be manufactured successfully by using the proposed method. To minimise the overall volume of support in a build, Leary et al. (2014) proposed a method to design ‘internal’ support-free optimal structures. First, a topologically optimised structure is derived and then the proposed method is employed to modify infeasible domains by adding extra material to their boundary to achieve self-supporting structures. In addition to optimising a part and its orientation, Hu et al. (2015) employed a shape optimisation model to trim down support structures.

3.1.2. Optimal build orientation

AM build orientation can have a significant influence on the final printed parts as well as support structures (DebRoy et al. 2018; Di Angelo et al. 2020; Keshavarzkermani et al. 2019; Sun et al. 2021; Zeng 2015). Different spatial orientations of a part cause different overhang areas over a substrate and consequently, different volumes of support structures are needed to fabricate the part, as shown in Figure 10(a).

Figure 10. (a) Different orientations resulting in different support structure volumes (Di Angelo et al. 2020). Optimisation of build orientation to minimise residual stresses using cubic lattice structure, (b) optimal orientation with cubic lattices (c) normalised residual stresses after process simulation. Reproduced with permission from Ref. (Cheng and To 2019). Copyright 2019, Elsevier.

Zhang et al. (2015a) developed a perceptual model to find optimal printing directions that can preserve important visual features. Hu et al. (2015) proposed a method to optimise an original model and its orientation to make it more self-supported. Zhang et al. (2015b) developed a multi-part orientation optimisation method, which is based on a genetic algorithm to find the minimal total build time and cost at an optimal global level.

The optimisation of support structures is important because it can minimise not only the material used but scan time (Dunbar 2016). Cheng and To (2019) proposed a method to minimise residual stress and support volume by optimising the build orientation – Figure 10(a,b). Di Angelo et al. (2020) provided a comprehensive review of the optimal build direction in AM and how the orientation influences part quality, surface quality, support structure, build time, manufacturing cost, and mechanical properties. Therefore, for more information on the build orientation optimisation, the reader is referred to (Di Angelo et al. 2020).

3.2. Support structures for thermal load

Support structures can help dissipate process heat and alleviate locally accumulated heat; therefore, they have the potential to minimise geometrical distortions caused by thermal stress (Blakey-Milner et al. 2021; Zhou et al. 2019a; Calignano 2014; Cheng and Chou 2020).

Leary et al. (2019) investigated the mechanical strength and thermal properties of AlSi10Mg LPBF support structures and found that the strength of a support structure is inversely proportional to its height and the heat transfer capability increases with smaller support spacings. Ganesh-Ram et al. (2021) found that unsupported overhangs can have effects on the microstructures of the printed parts as well as the hardness due to the different heat accumulation and dissipation. Moreover, support structures influence the fatigue strength of LPBF parts. Kajima et al. (2018) found that adding support structures can improve the fatigue strength of LPBF parts. The improvement is two folds: first, support structures reduced the residual strain which helped to prevent micro-cracks, second, support structures could dissipate heat faster which enabled the formation of finer microstructures contributing to better fatigue strength of the part.

To prevent overheating and increase heat dissipation, researchers have also employed TO to design optimum support structures for PBF. Traditionally, heat transfer TO has been widely used to design heat sinks based on various boundary conditions and objectives (Bendsøe et al. 2011; Alexandersen et al. 2016; Dede et al. 2015; Bruns 2007; Gao et al. 2008; Dbouk 2017; Lohan et al. 2019). However, there are much fewer works for AM. Allaire and Bogosel (2018) proposed a level-set TO approach to optimise the heat dissipation and cooling effects of support structures by using a spectral model. Zhou et al. (2019a) proposed the integration of a transient heat transfer model into density-based TO to design support structures shown in Figure 11(a) to efficiently transfer laser-induced heat to a prescribed heat sink, where an overhang constraint was incorporated to avoid overhang features in both supports and parts. Wang and Qian (2020) proposed a quasi-static boundary-dependent heat conduction model that only applies heat flux to overhanging areas to simplify the layer-by-layer process and employed density-based TO to generate optimal self-support support structures. Recently, Miki and Nishiwaki (2022) developed a model to design support structures to improve heat dissipation in the printing process. They incorporated a computationally inexpensive analytical model that uses the volume heat flux as a heat source for TO; their optimised support structure is shown in Figure 11(b).

Figure 11. Optimised support structures considering maximum heat dissipation, (a) results from Zhou et al. (Zhou et al. 2019a). Reproduced with permission from Ref. (Zhou et al. 2019a). Copyright 2019, Elsevier., (b) results from Miki and Nishiwaki (Miki and Nishiwaki 2022). Reproduced with permission from Ref. (Miki and Nishiwaki 2022). Copyright 2022, Elsevier.

3.3. Support structure for residual-stress load

The importance of support structures also manifests in preventing part distortion in MAM. Thermal-based MAM is similar to a welding process where there is a moving heat source that moves along the laser or electron beam scanning path (Luo and Zhao 2018; Zhang et al. 2019a). Therefore, the melting and solidification phenomena happening on the material can lead to high thermal stress and part distortion (Frazier 2014). Residual stress is reported to induce cracking, delamination, and distortion in MAM (Fang et al. 2020; Mercelis and Kruth 2006; Vrancken et al. 2014), typically spawned by the uneven rapid heating and cooling process. In-situ distortion could cause part-recoater collision and failure of printing. To consider the residual stress and distortion in the design stage, MAM process numerical modelling is significant.

The MAM numerical modelling can be categorised into micro-structure modelling (Sahoo and Chou 2014; Körner et al. 2020; Li et al. 2020c), particle-level modelling (Megahed et al. 2016; Stavropoulos and Foteinopoulos 2018; Cook and Murphy 2020) and continuum modelling (Srivastava et al. 2020a; Bayat et al. 2021; Luo and Zhao 2018). However, the first two are too time-consuming to be used in TO because TO would require hundreds of LPBF process simulations in its iterative process. Therefore, macro-scale models have enjoyed increasing attention in TO due to their shorter simulation times and acceptable prediction accuracies. Wildman and Gaynor (2017) incorporated a macro-scale thermomechanical model into TO to minimise the compliance of structures under the process-induced thermal load.

Moreover, one of the most famous macro-scale methods is the Inherent Strain Method (ISM), which was first proposed by Ueda et al. (1988), and it has been widely employed because of its efficiency and accuracy in predicting MAM parts’ deflections (Keller and Ploshikhin 2014; Siewert et al. 2019; Yaghi et al. 2018; Li et al. 2016b). It is also based on the element-birth method; it requires experimentally calibrated inherent strain values and a pure elastic mechanical simulation instead of a thermomechanical simulation, resulting in high computational efficiency. By incorporating ISM into TO, researchers have designed higher-performance structures that can reduce structural distortions and/or recoater-collision failure during the MAM process (Cheng et al. 2019a; Bartsch et al. 2019; Zhang et al. 2020a; Misiun 2021). Bartsch et al. (2019) proposed a two-step approach to design support structures in LPBF. The maximum forces obtained by a printing simulation in Amphyon® were transferred into the TO model in Comsol^® to reduce the distortions in the LPBF manufacturing process. Cheng et al. (2019a) developed a stress-constraint-based methodology to design lattice support structures to reduce the maximum residual stress caused during LPBF. An in-house code and Simufact® were used to establish the workflow shown in Figure 12, and the results were validated by experiments.

Figure 12. Workflow process for the implant component. (a) Specimen for printing, (b) voxel-based mesh for analysis, (c) Optimised density profile of support structure, and (d) Optimal lattice support along with CAD model of the component. Reproduced with permission from Ref (Cheng et al. 2019a). Copyright 2019, Elsevier.

Pellens et al. (2020) invented a method that employs ISM to get the vertical deformations and added the deformations of each printing layer as constraints in TO to achieve distortion reduction. Allaire et al. (2020) also considered two loading situations: gravity and thermoelastic load and the thermoelastic load only. Simufact Additive® software was used to simulate the AM process. Zhang et al. (2020b) proposed a support structure design method by using parallel-computing TO based on the inherent strain method, as shown in Figure 13, and found that the deflection of printed cantilevers can be reduced to over 60% compared to the original equipment manufacturer’s support structures. It was concluded that a stiffer support structure in terms of residual stress loading can lead to a lower deflection. An analytical explanation was also provided and is in good agreement with the numerical and experimental results.

Figure 13. Support TO results designed by Zhang et al. (2020a) considering the MAM process to reduce part deflection. (a) Original Equipment Manufacturer support, (b) support optimised for part gravity load only, (c) support optimised for both part gravity and residual stress from AM process. Reproduced with permission from Ref (Zhang et al. 2020a). Copyright 2020, Springer Nature.

In the following brief discussion, the reasons why the aforementioned efforts can reduce the distortion of a part in its as-built condition and after support removal is presented.

van Belle et al. (2013) found that support structures in MAM can significantly influence the residual stresses in the printed parts. The influence of the support structures on the printed part’s residual stresses was investigated and it was found that a thinner support structure could induce larger residual stress. Hussein et al. (2013) studied the effects of different lattice support structures on part deformation and different volume fractions and cell sizes were also investigated experimentally. It was found that smaller cell sizes and larger volume fractions (stiffer support structures) can lead to smaller deformations. Morand (2021) investigated the influence of supports on MAM parts. Several support patterns were pre-designed and compared. It was observed that the Y-shaped structure could reduce both part deformation and material usage significantly. It is interesting to note that this Y-shaped support structure is of great similarity compared to the support structures derived by Zhang et al. (2020b) using TO, as shown in Figure 13. Pan et al. (2020a) examined the effects of support structures on part deformation and found that the support hatch spacing and support contact spacing are dominant in the deformation of the final built parts. It was observed that a smaller support hatch spacing and a larger support contact spacing led to smaller deflections which implied that stiffer support structures lead to reductions in deformation. Recently, Xie et al. (2021) and Xie et al. (2018) proposed a constraining force theory to explain the distortions in laser additive manufacturing and applied it to investigate the influence of support structures on cantilever distortions. It was noted that a stiffer support structure could reduce the distortion of printed parts because a stiffer support structure influences lower strains on the previously deposited material induced by the newly deposited layer. This leads to a smaller bending moment and, thus, a smaller distortion after support removal. This is in agreement with the work of Zhang et al. (2020b). Finally, efforts on support structure TO are summarised in Table 1.

Table 1. Summary of efforts on support structure TO.

Topic	References	Descriptions
Gravity load	Pandey et al. (2004)	Weighted-averaging multi-criteria genetic algorithm to minimise support structure and build time
	Zhang et al. (2015a)	A perceptual model to find optimal printing directions that can preserve important visual features
	Hu et al. (2015)	Optimise the original model and its orientation to make support structures slimmed.
	Zhang et al. (2015b)	A multi-part orientation optimisation method
	Dunbar (2016)	Minimise scan time
	Calignano (2014)	Optimising supports structures by using experimentally statistical design
	Leary et al. (2014)	Design support-free optimal structures by adding extra material to their boundary to achieve self-supporting structures.
	Cheng and To (2019)	Minimise residual stress and support volume by optimisation build orientation
	Di Angelo et al. (2020)	A comprehensive review on the optimal build direction in AM
	Gaynor and Guest (2016), van de Ven et al. (2020), Langelaar (2018), Langelaar (2016b), Gaynor and Guest (2014), Qian (2017), Johnson and Gaynor (2018), van de Ven et al. (2018), Barroqueiro et al. (2019), Wang et al. (2018b)	Overhang optimisation by implicit methods of overhang filters
	Qian (2017), Wang et al. (2021b), Kuo and Cheng (2019), Allaire et al. (2017), Mezzadri and Qian (2020), Garaigordobil et al. (2018), Garaigordobil et al. (2019), Zhang et al. (2019b), Zhang and Cheng (2020), Luo et al. (2020), Wang et al. (2018a)	Overhang optimisation by implicit methods of overhang constraints
	Liu and To (2017), Allaire et al. (2017), Wang et al. (2018a)	Use the level set function to define the boundary and impose overhang constraints.
	Guo et al. (2017), Zhou et al. (2016), Zhou et al. (2021), Wang et al. (2018a), Zhang et al. (2015d), Zhang et al. (2017), Zhang and Zhou (2018), Wein et al. (2020)	Overhang optimisation by explicit methods
	Jankovics et al. (2018), Li et al. (2016a), Mass and Amir (2017), Thore et al. (2019), van de Ven et al. (2018), Mirzendehdel and Suresh (2016), Cacace et al. (2017), Pellens et al. (2018), Zhao et al. (2020a)	Overhang optimisation by other methods
Thermal load	Allaire and Bogosel (2018)	A level-set TO to optimise the heat dissipation and cooling effects of support structures by using a spectral model
	Zhou et al. (2019a)	Integrate a transient heat transfer model into a density-based TO for designing support structures to efficiently transfer laser-induced heat to a prescribed heat sink
	Wang and Qian (2020)	A quasi-static boundary-dependent heat conduction model that only applies heat flux to overhang area to self-support support structures for overhang areas
	Miki and Nishiwaki (2022)	A model for designing support structures by incorporating a computationally inexpensive analytical model that uses the volume heat flux as a heat source for TO
Residual stress load	Wildman and Gaynor (2017)	A macro-scale thermomechanical model into TO to minimise the compliance of structures under the manufacture process-induced thermal load
	Cheng et al. (2019a), Bartsch et al. (2019), Zhang et al. (2020a), Misiun (2021)	Design support structures under residual stress load by using the inherent strain method.

In addition to considering process-induced residual stresses in TO using ISM or its variants, the hatching pattern which can significantly influence thermal gradients has been studied. Takezawa et al. (2022) and Chen et al. (2021a) studied the optimisation of hatching orientation and the use of an island scanning strategy, respectively, together with an ISM for residual stress prediction to alleviate in-situ and ex-situ deformations. The same authors, Takezawa et al. (2020) and Takezawa et al. (2021), also investigated the integration of ISM in a homogenisation-based TO model to obtain variable density lattice structures that limit process deformation. To design process-tailored self-supported structures, Xu et al. (2022) introduced Langelaar’s AM filter Langelaar (2016b) within an ISM-based residual stress-constrained TO approach.

There are a few studies that have focused on considering in-process residual stresses and/or deformation within TO of both the support structure and entire part geometry. Allaire and Jakabčin (2018) proposed residual stress constraints to prevent inducing these undesired effects and incorporated them into a level set TO algorithm by using an adjoint method. Yasin et al. (2018) investigated the minimisation of process-induced warpage in a protector cover using TO and the results showed a significant warpage reduction in the printed product. Miki and Yamada (2021) developed an analytical solution that accounts for the distortion in the TO approach. A two-dimensional design model is utilised for validation of their methodology. Misiun et al. (2021) considered recoater collision and part deformation constraints in their optimisation approach for the cantilever geometry shown in Figure 14.

Figure 14. Topology optimised cantilever design with distortion and recoater collision constraints (far left), x and y displacement plots of the resulting topology (middle and far right image respectively) (Misiun et al. 2021).

To our best knowledge, most researchers have investigated residual stress and deformation constraints derived from inherent strain process modelling and incorporated them into TO. Moving forward, it will be beneficial to investigate the result of integrating detailed thermo-mechanical process models in TO to ascertain how viable current simplified inherent strain models are in capturing the residual stress and/or deformation constraints.

3.4. Remarks

Support structures in MAM have significant effects on the success and/or quality of printed parts. Support structures have potential influences on the mechanical properties of MAM parts, including quasi-static properties (tension, hardness, torsion, impact strength, fracture toughness, creep), environmental effects (stress corrosion, hydrogen embrittlement, and corrosion fatigue), and dynamic properties (low/high cycle fatigue, creep-fatigue, and fatigue crack growth) (Lewandowski and Seifi 2016).

Research on manufacturability-based numerical modelling of TO parts should be further investigated. For instance, support structure modelling is key in attaining a robust MAM process model because support structures significantly influence the formation, or lack thereof, of cracks, curls, sags, or shrinkages (Jiang et al. 2018). Multi-physics multi-scale models of MAM are of importance to better understand the manufacturing process by providing feedback on the viability of the structural and material design. Therefore, they assist in mitigating issues such as geometric errors, potentially large residual stresses, porosities, cracks, and poor material properties (Michopoulos et al. 2021).

Recently, there has been an increasing number of review papers on MAM modelling. Table 1 summarises a list of available review papers on the modelling and simulation of MAM process simulation, a large portion of which was published recently in 2020 and 2021. In Table 2, review papers are categorised into 3 groups based on the model scale: microstructure modelling, particle-level modelling, and continuum modelling.

Table 2. Summary of review papers on MAM modelling.

Names	Year	Num. of ref.	Micro-structure modelling	Particle-level modelling	Continuum modelling
Zeng et al. (2012)	2012	75			✓
Sahoo and Chou (2014)	2014	49	✓
King et al. (2014)	2015	69		✓	✓
Megahed et al. (2016)	2016	93		✓	✓
Bikas et al. (2016b)	2016	98			✓
Markl and Körner (2016)	2016	127	✓	✓	✓
Schoinochoritis et al. (2016)	2017	105			✓
Liu et al. (2018b)	2018	128	✓	✓	✓
Stavropoulos and Foteinopoulos (2018)	2018	177		✓	✓
Luo and Zhao (2018)	2018	158			✓
Bandyopadhyay and Traxel (2018)	2018	134			✓
Li et al. (2019)	2019	55			✓
Cook and Murphy (2020)	2020	218		✓	✓
Gatsos et al. (2019)	2020	139			✓
Guan and Zhao (2020)	2020	199		✓	✓
Guo and Chen (2020)	2020	81	✓	✓	✓
Hajializadeh and Ince (2019)	2020	34			✓
Körner et al. (2020)	2020	118	✓
Li et al. (2020a)	2020	203	✓
Ninpetch et al. (2020)	2020	74			✓
Srivastava et al. (2020b)	2020	279			✓
Tan et al. (2019)	2020	146	✓
Bayat et al. (2021)	2021	211		✓	✓
Hashemi et al. (2021)	2021	305	✓	✓	✓
Kouraytem et al. (2021)	2021	119	✓	✓	✓

To link the MAM process simulation to TO, accelerated models should be considered in the future. Besides the ISM models that can accelerate the simulation, analytical models (Huang et al. 2019a; Huang et al. 2016; Huang et al. 2019b; Flint et al. 2018; Mirkoohi et al. 2018; Ning et al. 2019; Steuben et al. 2019; Mirkoohi et al. 2020a; Mirkoohi et al. 2020b; Mirkoohi et al. 2021; Bacciaglia et al. 2019; Carraturo et al. 2020; Yang et al. 2018; Yang, van Keulen, and Ayas 2020) are faster and could be considered in the future. The benefit of these analytical models over ISM is that they can generate the temperature distribution, which may be very helpful when considering a TO strategy related to the temperature gradient and cooling rates.

Besides the analytical models, parallel computing is a powerful tool to further accelerate numerical modelling (Zhang et al. 2020a; Borrvall and Petersson 2001; Fernández et al. 2020; Zhang et al. 2021). Moreover, machine-learning-based TO is a direction that accelerates optimisation and has acquired increasing attention from both academia and industry (Lei et al. 2019; Guo et al. 2021; Chandrasekhar and Suresh 2021). Lastly, the CAD software for designing support structures and how to design them are two main challenges to consider for future efforts because support structures are of complex shapes, usually lattice structures, which are not very suitable for most CAD tools (Bacciaglia et al. 2020; Torigaki and Fujitani 2000; Aremu et al. 2017). The voxel-based representation is advantageous in a double-pronged way: to obtain fast geometry manipulation and transfer topology-optimised results to a post-process simulation, e.g. MAM process simulation (Bacciaglia et al. 2020; Bacciaglia et al. 2019). The main advantage of voxelization lies in the possibility to perform design-through-analysis within a single, yet effective numerical environment and without the need to generate finite element meshes that conform to the boundary of the simulated artifact (Zhang et al. 2020a; Carraturo et al. 2020).

4. Manufacturability considerations

4.1. Overhang elimination

As identified in the previous section, in most thermal-based powder-bed MAM technologies, there needs to be enough material to act as support for successive layers to be printed. If there are regions with unsupported material (overhangs), removable supports will be added. However, this procedure adds material, takes more time, and also requires supports to be removed which then requires additional polishing and/or other post-processing methods. Therefore, substantial efforts have been exerted to minimise the need for support structures or generate support-free structures (Gaynor and Guest 2016; van de Ven et al. 2020; Wang et al. 2021b; Gaynor and Guest 2014; Qian 2017; Johnson and Gaynor 2018; van de Ven et al. 2018; Barroqueiro et al. 2019; Wang et al. 2018b; Zhou et al. 2021; Langelaar 2016b). Researchers have developed several methods that can be broadly categorised into two groups: implicit methods and explicit methods.

First, the implicit methods are designed to generate support-free structures by using overhang filters or constraint functions to impose a surface slope constraint. Many researchers studied overhang constraints and incorporated them into TO to design overhang-controlled parts. The implicit methods can be classified into two major groups: (a) overhang filters, where element densities are filtered layer by layer based on elementally coordinative relations (Gaynor and Guest 2016; van de Ven et al. 2020; Langelaar 2018; Gaynor and Guest 2014; Qian 2017; Johnson and Gaynor 2018; van de Ven et al. 2018; Barroqueiro et al. 2019; Wang et al. 2018b; Langelaar 2016b) or filtered as a whole to generate printable density field (van de Ven et al. 2020; van de Ven et al. 2018); (b) overhang constraint functions which use specific constraints formulas to suppress the overhang angles larger than a threshold value (Wang et al. 2021b; Kuo and Cheng 2019; Allaire et al. 2017; Qian 2017; Mezzadri and Qian 2020; Garaigordobil et al. 2018; Garaigordobil et al. 2019; Zhang et al. 2019b; Zhang and Cheng 2020; Luo et al. 2020; Wang et al. 2018a). The overhang constraint methods align with the filter methods as they also use the layer-wise idea to generate their functions. To be specific, they aggregate local constraints (point- or element-wise constraints) to form a global overhang angle regulation, where the local constraints rely on the density gradient information and the elementally coordinative relations. For instance, (Qian 2017; Mezzadri and Qian 2020; Luo et al. 2020) used a Heaviside-projected density gradient while (Garaigordobil et al. 2019; Zhang et al. 2019b; Zhang and Cheng 2020) estimated the boundary normal based on local elemental density. Several other efforts have also utilised the Heaviside density projection or versions of it (Qian 2017; Garaigordobil et al. 2018; Osanov and Guest 2017; da Silva et al. 2019).

Recently, (Wang et al. 2021b) utilised B-spline parameterisation to generate the gradient of the density field and proposed the use of two constraints for overhang angle control and V-shaped areas. The schematics of the two constraints are shown in Figure 15(a). Bi et al. (2020) developed a layer-wise geometric constraint to eliminate overhangs based on the BESO framework. Figure 15(b) shows the application of the constraint in designing an industrial frame compared to an optimised version without the constraint.

Figure 15. The application of overhang or self-supporting constraints in (a) the B-spline parameterised TO. Reproduced with permission from (Wang et al. 2021b). Copyright 2021, Elsevier, (b) the BESO-based TO. Reproduced with permission from (Bi et al. 2020). Copyright 2020, Elsevier.

Moreover, level-set methods provide another approach to identifying topological boundaries and imposing overhang constraints using level-set functions (Liu and To 2017; Allaire et al. 2017; Wang et al. 2018a). For example,Liu and To (2017) addressed the self-support manufacturability constraint through a multi-level set modelling to represent the different layers, ensuring each layer is self-supported.

Furthermore, explicit methods, which are also called feature-driven methods, are methodologies that consider the boundaries of an optimised structure as explicit boundary representations (Zhou et al. 2016; Guo et al. 2017; Zhou et al. 2021; Wang et al. 2018a; Zhang et al. 2015d; Zhang et al. 2017; Zhang and Zhou 2018; Wein et al. 2020). Guo et al. (2017) proposed the use of moving morphable components and moving morphable voids to solve the support-free problem in a geometrically explicit way. Zhang and Zhou (2018) proposed the use of polygonal features (basic primitive) to perform 2D self-supporting structure design. Recently, they extended their work to 3D structures and solved the well-known design problems with V-shaped regions by limiting the positions of solid features (Zhou et al. 2021). Wang et al. (2018b) created a constraint using the element (pixels) densities. Any pixel with not enough pixels under it is penalised.

For moving morphable components, the same definitions are reused from the previous section however the constraints are changed. Instead of the size constraints, the overhang constraints are adapted.

Some other efforts to control the formation of overhangs are presented. Jankovics et al. (2018) developed a code where they defined a surface area sensitivity that is a derivative of the surface area of each element with respect to its density. The surface area sensitivities are added to the compliance sensitivities to obtain a final topology.

Li et al. (2016a) developed a way to constrain low-inclined surfaces and avoid unprintable circles by converting them into ellipses. In their case, the constraint is applied after the optimisation. Mass and Amir (2017) restricted the minimum angle of features in a structure using truss optimisation, their procedure works as follows: a ground structure within the design space is optimised with a minimum angle restriction for all the struts. The resulting optimal truss is used as a skeleton onto which they create the continuum structure (based on FE). Only certain elements located at a certain distance from the skeleton are considered. Thore et al. (2019) opted for a penalty regulation to control overhangs. They slightly extend Langelaar’s approach by adding weight factors to penalise sharp corners within resulting topologies. van de Ven et al. (2018) created a filter that eliminates overhang zones. They achieved this using a continuous front propagation scheme to study the progression of the edges. Mirzendehdel and Suresh (2016) transformed the support structures elimination problem into a multi-objective multi-material TO problem by considering both part performance and support structure material function in a consolidated objective function. Cacace et al. (2017) developed a method to generate ad hoc chamfers to reduce the number of support structures based on the level-set method.

Pellens et al. (2018) investigated the combination of the minimum length scale and maximum overhang angle to demonstrate that the overhang angle can be controlled along with the minimum length scale. The paper presents two ways of going about it, the first way is by implementing a minimum length feature followed by a maximum overhang angle filter and the second way is by doing the same thing in reverse. Zhao et al. (2020a) used a convolution function to detect overhanging areas, and with that, generated support-free topology-optimised results. The time efficiency of their proposed convolution method is reported higher than the traditional enumeration method.

4.2. Process-, design-based geometrical considerations (minimum, maximum feature, and length control)

Enforcing a minimum feature size is a common constraint within TO (Mhapsekar et al. 2018; Gardan and Schneider 2015; Osanov and Guest 2017; Sigmund 2001; Zhang et al. 2016; Zhao et al. 2019; Zhou et al. 2015; Liu et al. 2019; Vatanabe et al. 2016; Carstensen and Guest 2013; Guest 2009a; Zhang et al. 2014; Guest et al. 2004; Weiss et al. 2021). The minimum feature size is enforced during optimisation to enable mesh independency and is also necessary to fulfil the requirements of the manufacturing process. Depending on the manufacturing process, some sizes are not attainable, and it is therefore important to enforce a restriction on such sizes.

To evaluate minimum and maximum feature controls, it is important to define filtering and projection in TO. Filtering is attributing a weight function to an element based on the neighbouring elements or nodes; the amount of neighbouring elements or nodes to consider is given by the minimum size provided by the user. Therefore, the actual density of an element can be rewritten based on the density of the neighbouring elements/nodes (Guest et al. 2004; Zhou et al. 2015). One typical way the minimum feature size is reached is by first applying a filter and then imposing the filter for every iteration. The minimum size which is imposed during filtering is achieved by deciding how far the last element will affect the current element. Filtering can be done using nodal densities instead of element densities. The main benefit of using nodal densities instead of element densities is the computational cost. In the case of nodal densities, filtering is used to define an element’s density based on the densities of the nodes which are located within a certain radius from that element. For a certain minimum feature size, it is possible to control the number of nodes that have to be considered. However, in the case where elements are used, elements cannot be skipped. This is because there needs to be a density for all of them. Hence, nodal techniques might improve the computational cost for specific conditions (Hussein et al. 2013).

Projection refers to classifying continuous inputs into a finite number of outputs (Sigmund 2001). In the TO context, the inputs are the densities of the elements of a discretized design with continuous volume fractions between 0 and 1 and the outputs are elements with volume fractions equal to 0 (void) or 1 (solid). Projection is achieved through functions like the Heaviside and Sigmoid or level-set functions.

Zhao et al. (2019) worked on developing porous structures with minimum feature sizes. The authors map topologically optimised geometry on top of unit cells. The TO algorithm they used includes filters that get rid of the need for support structures and another filter to impose a minimum feature size. The specificity of their algorithm is that the elements’ densities are referred to as unit cell volume fractions and when the cell becomes smaller, the volume fraction becomes greater. Qian (2017) used Helmholtz’s partial differential equation (PDE) to impose a minimum feature size. Gardan and Schneider (2015) designed an optimisation workflow to ensure that parts were properly printed. They derived a set of guidelines to couple T.O. with AM by introducing a penalisation factor to impose maximum thicknesses for different walls. Lazarov and Wang (2017) came up with a bandpass filter to restrict the appearance of too-thick or too-thin features. They used bandpass filters, originally used to limit frequencies, to limit the density of elements in the optimisation problem. Mhapsekar et al. (2018) offered a set of guidelines to minimise the number of thin features, support structures, and thus overhangs. While a density filter was utilised to minimise thin features, they applied a weighted multi-objective approach to minimise compliance and support structures.

Liu et al. (2019) discussed the implementation of minimum feature size for multiscale TO. In their words, multi-scale T.O. is ‘an adaptation of the homogenisation-based TO technique to design the local micro or mesoscale structural details of a part or without concurrently optimising the macro-scale structural geometry’. To observe how unit cells would behave, they experimented and concluded that the unit cell size should be selected to be considerably smaller than the part to ensure the homogenisation-based simulation’s accuracy but at the same time, it should be larger than the minimum length scale limit to reduce the impact of the length scale constraint. Osanov and Guest (2017) adjusted the Heaviside projection function to better consider the nature of the layer-by-layer AM process. They transformed the space of influence of neighbourhood elements/nodes from a sphere to a cylindrical shape. Vatanabe et al. (2016) studied the effect of a few manufacturing constraints on the final compliance of the optimised part. The constraints they considered are the minimum member size, and minimum hole size, amongst others. Guest et al. developed a projection method incorporating the nodal volume fractions instead of using the elemental volume fraction (Guest et al. 2004), the nodal volume fractions are then projected back onto the element’s centroid.

A TO framework that was developed to ensure a minimum feature size constraint is the moving morphable components (MMC) (Zhang et al. 2016). A similar method is moving morphable voids (MMV). The MMC method treats the design space as a set of components or geometrical features which can first be parameterised, then moved, and/or morphed. To satisfy the minimum length/size constraint, restrictions are applied on the minimum size, as well as the minimum intersection between two components.

The different MAM technologies offer different minimum size restrictions. Design guidelines for parts to be printed by LPBF, EBM, and BJ as outlined in Toyserkani et al. (2021) and Diegel et al. (2019) show that the resolvable minimum feature sizes should be 0.1 mm (0.3 mm for vertical walls), 0.5 mm (0.6 mm for vertical walls), and 1 to 3.2 mm (vertical walls inclusive), respectively. However, several variables can cause these minimum sizes to be inapplicable in a practical design case. In a design example shown in Figure 16, a structure that supports a thin feature in the printed framework has a delaminated support area as shown in the red box on the left image. The framework was printed by LPBF using Hastelloy X as material. Just before delamination, during printing, the aspect ratio of the underlying support structure was small as its width was significantly smaller than its height. The machine’s recoater had sufficient momentum to cause this slender support structure to shift its top position on the powder bed. This shift created a ditch in the region of the powder bed around the top of the slender support structure contributing to its delamination. This delamination contributed to poor heat conduction from the top layers to the substrate, inducing high residual stresses, and thereby resulting in a crack in the boss of the framework during support removal as shown in the right image of Figure 16. Therefore, it is insufficient to restrict a design to contain unsupported features with sizes close to the minimum allowable by the manufacturing technology as other variables such as support structure length, width, type, build orientation, etc, can adversely affect the build outcome. Lattice cells with strut or wall diameters close to the minimum allowable sizes are typically not seriously impacted by recoater movements since the strut aspect ratios are usually at acceptable values that limit flexing. Metrological experiments (McGregor et al. 2019; Rathore et al. 2021; Dallago et al. 2019; Noronha et al. 2022; Colosimo et al. 2022) conducted on as-printed strut-based lattices compared to as-designed models show that lattices with strut diameter sizes of 0.5 mm and aspect ratios of over 0.15 are printable without any major defects, however, with ‘overprints’ and ‘underprints’ at different locations.

Figure 16. An LPBF-manufactured topology-optimised framework before and after support removal.

Unlike maximum size control, minimum size control is critical from two standpoints: optimisation and manufacturability. For optimisation, it is implemented for mesh independency and to eliminate checkerboarding features; for manufacturability, it is implemented to guarantee feature resolution by a given manufacturing technology. Maximum size control, however, is important to give the designer better control of the structural features being formed. In 2009, Guest (2009b) considered the maximum length scale in mechanical and fluid-flow optimisation problems by placing a constraint on the phase composition of circular local regions throughout the design domains. Carstensen and Guest (2018) extended this work by providing nonlinear weighting functions to implement a two-phase minimum and maximum length scale control with the capabilities of actively projecting either the solid or void phases during the optimisation. In quite similar veins, Fernández et al. (2019) and Fernández et al. (2020) implemented maximum length controls as initially proposed by Guest (2009b) by projecting the void phases during optimisation. Lazarov and Wang (2017) used so-called morphological operators to impose a maximum length scale on designs during optimisation. In an attempt to eliminate the discrepancies that can arise between density-based TO results and reconstructed models, Costa et al. (2019) employed Non-Uniform Rational Basis splines (NURBS) hyper-surfaces to formulate the maximum length scale control.

4.3. Enclosed void elimination

Another important constraint is enclosed voids, and although less popular than the previous constraints presented, it has gotten some attention (Li et al. 2016a; Zhou and Zhang 2019; Liu et al. 2015; Zhou et al. 2019c; Zhou et al. 2019b). Such a constraint targets powder bed MAM such as laser and electron-beam powder bed fusion, binder jetting, etc where there are risks of entrapped powder particles within the printed optimised part. Establishing void connectivities is an approach to resolving enclosed voids. Succinctly expressed, imposing the connectivity of voids is akin to treating the outside of the structure as a ‘void’ and ensuring all internal voids are connected to it. Imposing a constraint on enclosed voids can be done through the Virtual Temperature Method (VTM) described by Liu et al. (2015). The VTM is inspired by heat transfer concepts and treats all enclosed cavities as heat sources, while the solid parts around the cavities are treated as insulators. They applied the enclosed void constraint in the optimisation of torsional cantilevers. They also optimised and printed the cantilever without the constraint; this resulted in the retention of internal support structures and powder as revealed in the sectioned cantilever. However, with the inclusion of the enclosed void constraint, the optimised structure ensured that the internal void was connected to the ‘outer void’ guaranteeing the removal of internal support structures and powder. Other efforts to exclude voids in parts designed by TO can be seen in Xiong et al. (2020), Luo et al. (2020), and Wang (2021a).

4.4. Remarks

In overhang elimination methods, there is one prevailing issue. An arbitrary minimum angle can be imposed during TO, however, this will not necessarily ensure acceptable manufacturability especially when the thicknesses or sizes of features within the printed part are considered. Some more effort should be placed to qualify the manufacturability of overhanging regions through a physics- or data-driven approach. Some algorithms such as the MMC, modify the geometry after the optimisation process, however, these modifications can potentially have undesirable changes on the optimisation objective. Some effort should be placed into investigating the resulting deviations.

5. Porous feature design

There are many forms of porous structures. Often, the results of many TO methods yield varying levels of structural porosities. Sometimes, pores are inserted voluntarily into a structure for lightweighting or other application-specific purposes. The structures that are discussed in this section follow this case. Porous structures can be divided into two broad categories. When holes are introduced with a clear repetitive pattern vs. when holes are introduced with no clear pattern. The sub-category of porous structures that exhibit a repetitive pattern is cellular structures and (Nsiempba et al. 2021) discusses them in detail. A subcategory of cellular structures is lattices.

5.1. Porous design strategies based on topology optimisation

This section will review specific TO methods for lightweighting, that produce solutions that functionally have similar features as those produced through latticing. In this context, latticing refers to filling the design volume with repeating unit cells.

Some approaches first use TO, followed by a post-processing step that adds lattices as done in Abdi et al. (2018). The work in Abdi et al. (2018) was done using the Isoline-Extended Finite Element Method (Iso-XFEM) to obtain smoother boundaries in conjunction with BESO (likened to a discrete implementation of the SIMP method Plocher and Panesar (2019)). The BESO method can be used to optimise lattices by assigning the degrees of freedom as the lattice thicknesses to optimise the lattice for maximum stiffness and a fixed mass (Tang et al. 2015).

The use of cellular structures through latticing as displayed in literature is mainly for light-weighting and to meet up with design objectives such as heat transfer and energy dissipation (Plocher and Panesar 2019). Heterogeneous periodic lattices can be optimised for maximum stiffness by homogenising unit cells into representative volume finite elements (Khanoki and Pasini 2012). The same type of lattices can also be designed by mapping the obtained density obtained by the SIMP method to a lattice cell with a certain volume fraction (Alzahrani et al. 2015).

A way of generating features in a structure like a heterogeneous and pseudo-periodic lattice is the volume constraint modified SIMP method that implicitly considers a maximum volume fraction in a prescribed local region within the design domain done by Wu et al. (2018). The application for this method was for infill design for AM parts with a fixed external shell. In this method, the global volume constraint typically used in the SIMP method is replaced by a local volume constraint, that has a similar form to the typical SIMP local filtering function but with a weighting of 1 for all neighbourhood cells (Wu et al. 2018). Another observation made was that the pseudo-periodic lattice struts have an alignment along stress trajectories, also seen in the human femur bone. The article highlights two features of the SIMP method used to produce a pseudo-periodic lattice, and only for load-bearing applications; robustness to local failure and force variations, which often occur in practical load cases. The robustness to local failure was shown clearly by locally removing material along a vertical line. It was also shown that a pseudo-periodic lattice that is conformal to the stress field has better compliance as well as robustness to local failure compared to a periodic lattice.

Different values of the constants used in the optimisation problem can be used to suppress the formation of wall-like structures instead of trusses. The results given in Wu et al. (2018) are qualitatively similar to the ones that can be obtained using the commercially available ParaMatters software (Bogomolny 2018). The work by Wu et al. (2019) extends the work in Wu et al. (2018), by generating a lattice with constant cross-section trusses, having more of them in higher principal stress regions. This is argued to generate results that are more manufacturable by AM. It is also comparatively faster to compute than the local volume constraint method described in Wu et al. (2018) since one finite element corresponds to a lattice cell.

Based on the observation in Wu et al. (2018) that the resulting TO result produces lattice struts aligned with the stress trajectories, another avenue of research is to use the stress trajectories themselves to produce a pseudo-periodic lattice directly; this requires solving only one FEA step to obtain the stress field and would be easier to manufacture by using standard strut geometries. The first article using this approach is by Reinhart and Teufelhart (2013). The method is summarised as follows:

1. Run an FEA simulation with the design space and the design loading conditions.

2. From the obtained data calculate the principal stresses for each node.

3. Using the designer’s input decide on initial points close to the applied loads and from it calculate a line of force or flux line such that its path is always parallel to an interpolated principal stress direction.

4. Using designer’s input, join the lines of force and add cross trusses to make a lattice structure.

5. Using an optimisation method adjust the thickness of the struts such that the structure’s compliance and/or maximum Von Misses stresses are minimised.

A structure obtained using the proposed method was very similar to a Michell strut system. As described, the method was applied to a horizontal beam with a downward end load and the algorithm requires user intervention. Another work done by Daynes et al. (2017) follows the same procedure. The method uses Altair OptiStruct 13.0^® to calculate the stress field in the design space after topology optimisation without an interpolation function, the lattice is constructed in MATLAB and the resulting lattice is size optimised also using OptiStruct. The force lines are found by manually specifying the initial points and integrating them using interpolated stress field values from finite elements and the Euler method. The key difference here from (Reinhart and Teufelhart 2013) is that the stress distribution is from a resulting topology-optimised solution, using no interpolation to promote a high-contrast solution. Another observed difference is that the resulting quadrilateral lattice cells were subsequently filled with another truss cell design. A graphical abstract of the method from (Daynes et al. 2017) is shown in Figure 17. In addition to the use of force lines or stress fields, another popular approach to implementing infill TO-MAM structures is the variable density cellular approach, used by Zhang et al. (2015c) and Cheng et al. (2017) for stiffness maximisation and Takezawa et al. (2019) for effective liquid cooling.

Figure 17. Force line method and resulting lattice for a beam in bending as described in Daynes et al. (2017). Reproduced with permission from (Daynes et al. 2017). Copyright 2022, Elsevier.

More recent work by Arora et al. (2019) automatically extracts a Michell truss structure from the stress field. This is done by ‘smoothing’ the stress field obtained from linear tetrahedral elements before using the field to produce the lattice. This is done by generating a quadrilateral mesh with a custom mesh generation algorithm and using the stress field as an input. The resulting quadrilateral element edges are also aligned with the stress field. The obtained structures are also very similar to a Michell strut system. The method only extracts a lattice structure with a uniform thickness and does not do sizing optimisation as a final step. The resulting lattices from these methods can be further optimised by adjusting the thickness of the struts. Although the optimised porous structures gene, (Reinhart and Teufelhart 2013; Daynes et al. 2017) were validated by printing the resulting geometries, they were only printed in plastic which is less challenging than printing them in metal. Although much work has been done to improve the printability of TO-generated geometries and repeating lattices, there are ample research opportunities for further optimisation. The strut dimensions can be further optimised as a post-processing step; possibly using a gradient-based method like in SIMP for example but with the optimisation variables being the strut thicknesses, and using an FEA solution for a frame structure with fixed lattice nodes. Additionally, LPBF fabrication constraints can either be integrated within the algorithms or introduced as post-processing steps.

Other efforts to consider strut-like porous structures within topology optimisation for metal additive manufacturing can be seen in the work by Lin et al. (2007) who adopted a dual TO approach. The dual approach consisted of a macroscopic or first-scale TO to obtain the density design field while the second approach involved a homogenisation method to design the microstructure and come up with effective and specific elastic properties across the porous design. In the study, lumbar interbody fusion cages were printed via LBPF using Ti6Al4V to show the potential of the proposed methodology. In a similar effort by Xiao et al. (2013), the homogenisation method was used to design load-bearing bone implants having high stiffness and relatively large porosities to encourage bone ingrowth. Results showed improvements in the computationally tested elastic modulus of the optimised scaffolds compared to more standardised cubic scaffolds. Schwerdtfeger et al. (2011) and Takezawa et al. (2017) also utilise homogenisation-based TO to implement auxetic and porous structures, for compliant mechanisms and to obtain high stiffness and strength steels respectively, through powder-bed AM processes.

Another research effort within the past couple of years is the combination of TO and surface-based or triply periodic minimal surface (TPMS) lattices to obtain functionally graded porous structures. Although this area is beyond the scope of this work considering TO is typically not used to directly generate the minimal surfaces, some recent works are noteworthy. Strömberg (2022) proposed a TO framework that provides a macro layout for the design problem and a relative density field for an infill surface lattice structure. To gain more control over TPMS lattices, Hu et al. (2022) utilised TO to optimise the scale distribution of graded shell-infill walled gyroid structures. A novelty in this study is the functions that were developed to represent, analyse, optimise, and store information thereby avoiding remeshing the structure upon a design change. Relative density mapping to manipulate unit cell volume fractions is one of the most popular approaches in obtaining graded TPMS designs as observed in Zhang et al. (2022), el Khadiri et al. (2022), Alkebsi et al. (2021), and Ren et al. (2021) while the use of TO and TPMS for thermo-fluid/thermal-based applications is conducted in Wang et al. (2022) and Yeranee et al. (2022). Most of the aforementioned efforts were conducted within the last 2 years and understandably, they are mostly numerical/theoretical with little or no experimental verification. While these methodologies are in their infancy, it is a good practice to commence manufacturability and mechanical studies on resulting designs early on to tweak the algorithms where necessary. For example, results from the study by Hu et al. (2022) often give ‘stretched’ and/or thin wall surfaces that might not be well supported against gravity or well connected for heat conduction for a build orientation perpendicular to their longitudinal axes.

5.2. Remarks

One challenge of leveraging TO for metal 3D printing is making sure the topologically optimised design is manufacturable. A recent work that attempts to find an optimised shape that is designed not to fail during printing is (Misiun et al. 2021) which included an inherent strain mechanical model to take into account distortion after separation from the build plate and re-coater collisions. A review of a similar previous technique referred to as ‘space-time’ TO for wire-fed directed energy deposition is described in Wang et al. (2020b). These techniques use a simpler model to take into account the self-weight of intermediate structures, process-dependent loads, and time-dependent mechanical properties such as a curing process. More efforts in this direction are expected in the future, especially with the increase in powerful computing resources. The use of models inspired by the physics of the printing process might be more beneficial rather than an observation-driven metric such as overhang constraint angles (Leary et al. 2014).

6. Artificial intelligence-assisted design

The conventional TO process usually requires several iterations in the order of tens to hundreds to arrive at an optimal design and each iteration can be computationally expensive, especially for high-resolution applications. Machine Learning (ML) models, especially deep learning, can be used to drastically reduce the computational time since when well-trained, can compute several design problems quickly without undergoing the iterative process of conventional TO methods. Several researchers have employed deep learning-based methods for TO: Sosnovik and Oseledets (2019) employed a convolutional neural network (autoencoder-type network) trained with intermediate topologies received from conventional TO approaches. The optimisation problem was modelled as an image segmentation task with the inputs into the network consisting of two greyscale images (2-channel image) with one channel containing the density distribution of an iterated solution from a regular TO solver. The second channel contained the last gradient update of the densities of the last performed iteration. The model prediction is a greyscale image of the predicted final structure; their proposed model is shown in Figure 18(a). The results showed that the encoder-decoder architecture could predict optimised structures up to 20 times faster with few pixel-wise changes compared to the standard simplified isotropic material with penalisation (SIMP) approach. The methodology was also shown to solve heat conduction problems, outperforming SIMP results both in speed and binary accuracy-wise with thresholding. Banga et al. (2018) extended the encoder-decoder CNN architecture to generate 3D structures. Their approach involves the use of an FEA-based TO software, TopOpt (Aage et al. 2015), based on the SIMP method to generate structures from the initial TO iterations. The optimisation process is then stopped at an intermediate stage after which the current structure from the process is fed into the CNN network to predict the final structure. The input into the network includes the 3D density distribution of the conventional TO, gradient voxel densities between iterations, forces, and boundary conditions along x, y, and z directions. The results showed that a trained network architecture can predict the final structures instantaneously with an average binary accuracy of 96.2%- and 40%-time reduction as compared to solely using the FEA-based SIMP method. In Abueidda et al. (2020), they also utilised CNNs to predict optimised structures for a given set of boundary conditions, loads and optimisation constraints. They considered materials with hyper-elastic responses having material and geometric nonlinearities. The dataset used in training the model is composed of optimised designs and their corresponding boundary conditions, load, and volume constraint from conventional topology optimisers. Preliminarily results showed CNN could derive optimised results with much less computational costs.

Figure 18. Application of deep-learning-based models (a) CNN used for prediction of optimised structures from intermediate topologies (Sosnovik and Oseledets 2019) (b) GANs for TO (Rawat and Shen 2018).

Generative modelling (Creswell et al. 2018) is a very exciting field that has several diverse applications. Generative Adversarial Networks (GANs) are unsupervised machine learning methods that automatically find parameters that model high-dimensional data and generate new data from sampling the distribution. Yu et al. (2018) applied a deep learning-based approach to generative modelling. This was done by applying GANs to generate optimised structures without TO iterations. They used a type of generative network called the variational autoencoder (VAE). The encoder section of their network extracted relevant features from the input space to derive the mean and variance latent variables that enabled several optimised structures. Although their model to predict test cases was devoid of gradient-based TO processes, all training data was generated from the SIMP TO method. The drawback of this approach is the computational time required in generating the training data. Rawat and Shen (2018) also employed GANs to generate optimised structures for certain constraints and conditions. The training dataset was also gotten from a conventional TO code which uses the SIMP model. In comparison to other existing conventional algorithms, their approach showed the capability of generating sub-optimal topology with a relatively small training dataset. An optimised topology from their GAN model compared to a reference ground truth is shown in Figure 18(b).

Another application of machine learning in TO is parameter tuning. Lynch et al. (2019) introduced a machine-learning framework to derive optimal parameters in TO. The framework involves a two-step process where a recommendation of parameters is first derived from similar domain problems to serve as the training data for the next step which involves using Bayesian optimisation to refine the parameters for a specific TO problem. The authors developed a quality metric to quantify the robustness of the solution and applied it to simple optimisation problems. The approach was shown to be less computationally expensive, and the application to more complex TO problems was reserved for future work.

The aforementioned efforts focused on optimising structures without manufacturing considerations. A research effort oriented to part manufacturability by LPBF is seen in the work by Naresh et al. (2021). They applied a 3D-Unet CNN-based attention architecture to optimise LPBF-manufactured parts against in-process cracking; their methodology is expressed in Figure 19. Their approach involved formulating the optimisation task as a segmentation problem where training inputs were derived from conventional TO methods or simulators. These inputs were fed into a 3D attention Unet architecture to predict optimised structures in compliance with either the maximum shear strain index (MSSI), strain failure index (SFI), or total strain energy density index (TSI), with the conclusion of MSSI as the best index for predicting the likelihood of cracks. The unique aspect of their approach involves the use of weights from the penultimate network layer to generate maps that focused on regions most relevant to accurate crack index estimation. Their framework demonstrated the effectiveness of CNN-based methods to derive optimised structural parts for LPBF with reduced MSSI values and minimal computational time.

Figure 19. A PATO framework to integrate additive manufacturability in the part design process through a deep neural network predictor (Naresh et al. 2021).

In the background of these aforementioned successes, a recent robust and critical review on the use of artificial intelligence in topology optimisation was done by Woldseth et al. (2022) from the famous TopOpt group led by Ole Sigmund. An important observation made was the many direct AI design models for TO in literature and it was argued that these models often generate poor designs which are costly to obtain with a limited problem and mesh generality. It was suggested that the use of AI to attempt to provide iteration-free TO models should be abandoned while the focus should be placed on alleviating the computational cost of portions within the iterative process. The study also suggested that investments should be made in improving physics-informed neural networks (PINNs) for TO and neural network models for result post-processing.

In reflection, deep-learning methods especially CNNs are quite promising in deriving optimal structures with minimal computation time. These methods are heavily dependent on the numerical solutions from conventional TO methods thus the accuracy of these deep-learning approaches is limited to the quality of the dataset used in training these models. Nevertheless, they show high potential for practical use cases and thus require further studies. Consequently, in the short term, the focus should be placed on physics-influenced models such that there is less dependence on the results of conventional TO methods as sole ML inputs. Rather, the physics governing the TO problem and objective/constraint sensitivity analysis can be captured within the ML model. There is also the need to explore high-resolution 2D and 3D structural problems that will ensure these models become useful within the DfAM framework. In the long term, the aim will be to allow AI-driven TO models to solve structural design problems for part performance as well as manufacturability.

7. Simulation and software capabilities

Several software tools can now assist in the DfAM workflow by addressing at least one of its stages as shown in Figure 20. The first stage in the DfAM workflow shown is pre-processing, which involves creating a three-dimensional (3D) model and defining the design space, after which TO can be set up and run. Once an optimal design is generated, its 3D model can be modified and refined in the post-processing step to meet any form, fit, function, and DfAM requirements. The final steps involve validation of the model via numerical or analytical approaches, after which the optimisation may be redefined and repeated as desired, or the design can be finalised. Simulation of MAM processes can also be used to predict any fabrication issues and inform design changes. In this section, we present and compare a range of software tools for TO and MAM process simulation.

Figure 20. TO workflow with major steps. (a) Pre-processing design space and boundary condition defining using a color-coding representation (Ibhadode et al. 2021) and a voxelization approach (Zhang et al. 2021) (reproduced with permission from (Zhang et al. 2021). Copyright 2021, Springer Nature) (b) topology optimised models (Ibhadode et al. 2021; Zhang et al. 2021) (c) Post-processing step to smoothen a topology optimised connecting rod model generated in nTopology (nTopology 2023) (d) Different length scales and models required to model MAM processes. Reproduced with permission from (Francois et al. 2017). Copyright 2017, Elsevier. (e) Prediction of hot and cold defects for PBF processes using a probability of thermal errors. Reproduced with permission from (Moran et al. 2021). Copyright 2021, Elsevier.

7.1. Open-source software and frameworks

There are several open-source tools with complete workflows for TO (Aage et al. 2015; Zhang et al. 2021; Aranda et al. 2020; Kambampati et al. 2018; Vogiatzis et al. 2017). Some provide a nice user interface (UI) and allow defining two-dimensional (2D) or three-dimensional (3D) problems for objective functions such as compliance minimisation (Zhang et al. 2021; Aranda et al. 2020; Smith and Norato 2020) and global temperature minimisation (Zhang et al. 2021). Ease of use and accessibility are typically prioritised so new users can familiarise themselves with TO and its workflows quickly. However, open-source tools that address workflow steps in a modular approach, such that they can be coupled with other tools, are particularly advantageous (Kambampati et al. 2018; Talischi et al. 2012). By creating tools that address discrete parts of a workflow, they can be interchanged conveniently to give developers fast access to recent developments in TO research. Here, examples of open-source software that address at least one of these steps in TO workflows are reviewed: pre-processing, TO, post-processing, and AM simulation.

7.1.1. Pre-processing tools

Pre-processing for TO involves a preliminary definition of the optimisation problem by creating a 3D model and designating the design space. This step can be mainly satisfied by general open-source CAD (Hennes 2022; Kintel 2022; Kazakov 2022) and meshing tools (Kazakov 2022; Geuzaine and Remacle 2009; Si 2015; Mahadevan et al. 2022), so open-source pre-processing tools made specifically for TO workflows are rare. One pre-processing tool developed by Ibhadode et al. (2021) provides a colour-coded visual UI to improve accessibility. Both the design space and boundary conditions (BCs) for structural optimisation problems are definable using a color-coding representation in a 2D grid, see Figure 20(a). As problem complexity increases for 3D geometries with many multi-physics constraints, the utility of this representation increases its convenience for helping the user identify and edit constraints. However, this requires effective communication of BCs to any downstream tools. As well, Zhang et al. (2021) developed a parallel computing TO framework named TopADD, which expands on Aage et al’s framework (Aage et al. 2015) and provides classes for pre-processing, see Figure 20(a,b). These classes provide functionality for importing and voxelizing design domains as STL files and accommodate 2D and 3D dimensionality. This gives the designer freedom in initialising complex design domains beyond simple solid geometry primitives (cubes, spheres, etc.). This framework expansion is designed to handle linear compliance and heat conduction design problems. Similarly, Aranda et al. (2020) developed a pre-processing tool for linear compliance and volume minimisation TO problems with their software TOptimiz3D. This requires a design domain mesh to be generated before importing to TOptimiz3D, where constraints, boundary conditions, material properties, and optimisation parameters can be defined. Since these pre-processing tools are limited to linear FEA, more complex bending loads will be harder to simulate, leading to less accurate optimisation results.

7.1.2. Topology optimisation: PDE solvers and processing tools

Many open-source codes implementing new TO strategies are made available in literature and have recently been reviewed in Zhang et al. (2021), Ribeiro et al. (2021), and Deng et al. (2021). These codes generally implement a new technique and solve several benchmark problems to characterise their effectiveness, though they can be adapted to different problems. Open-source codes that focus on implementing AM-specific constraints (feature size, build direction, overhang constraints, etc.) were investigated in literature and found to be rare. One example is a tool developed in C++ (Amir and Amir 2021), which minimises compliance while improving printability by adding lattice supports. Several example structures are completed in 3D for different build directions, and lattices are only added when they do not significantly alter compliance (Amir and Amir 2021). Overall, there is a current need for more open-source codes implementing AM constraints in TO.

To enable solving applications of greater complexity and scale (e.g. 3D multi-physics optimisation), powerful tools for PDE solving are needed. Open-source toolkits and libraries can be implemented for these purposes, which should address requirements such as efficiency, speed, and accuracy (Meng et al. 2020; Morse et al. 2021; Li and Chen 2018). Ideally, they also allow users to develop custom objective functions and constraints for specialised problems. To meet these criteria while achieving modularity, open-source PDE solvers such as FEniCS (Alnæs et al. 2015) and FreeFEM (le Hyaric et al. 2022) are currently very popular in TO research, being used recently in Laurain (2018), Sá et al. (2021), Alonso et al. (2019), Sun et al. (2020), Miki and Nishiwaki (2022), Kim et al. (2020), Zhu et al. (2021a), Jung et al. (2021), Li et al. (2021), and Li et al. (2022), respectively. These PDE solvers offer high-performance computing (HPC) and parallel processing to enhance their solution speed and handle computationally demanding problems. A similar powerful PDE solver is deal.II (Arndt et al. 2021), which also offers parallel processing capability for many varieties and orders of FE elements. However, some more modern functionalities such as HPC are not yet provided by deal.II. Another advanced PDE solver toolkit is MFEM (Anderson et al. 2021), which enables parallel scalable processing to thousands of cores, efficient high-performance computing (HPC), graphics processing unit (GPU) acceleration, and strong, diverse meshing capabilities. These tools present a significant incentive for MFEM’s use in TO research, which has been done in White et al. (2020) and White et al. (2018). To enable parallel processing and GPU acceleration, the PDE toolkit is PETSc (Balay et al. 2021) is very popular, having been used for TO applications in structural and DfAM applications (Amir and Amir 2021), fluid dynamics (Høghøj et al. 2020; Lazarov et al. 2018), and heat transfer problems (Zhang et al. 2021; Høghøj et al. 2020; Lazarov et al. 2018). For more flexible multi-physics coupling using different solvers, the coupling library preCICE (Bungartz et al. 2016) can be used to facilitate communication, and already has official adapters for several popular solvers. A great advantage of this library is its intentional modularity in its design, which allows simple coupling with black box solvers without requiring significant solver code changes. This enables easy incorporation of custom in-house tools. For examples of other open-source toolkits and libraries, we refer the reader to OpenMDAO (Gray et al. 2019), DUNE (Bastian et al. 2021), OpenFOAM (OpenCFD and ESI Group 2021), and libMesh (Kirk et al. 2006).

7.1.3. Post-processing and AM simulation

Post-processing involves altering and exporting the optimised geometry so that it can be re-designed, modelled for validation, and manufactured (Subedi et al. 2020). Surface-based representations generated by TO tools regularly require secondary operations such as smoothing or remeshing to improve surface quality. In addition to the open-source meshing tools mentioned in 7.1.1, CGAL (Project 2021) and TTK (Bin Masood et al. 2021) offer many powerful capabilities including polygonal reconstruction, mesh segmentation, simplification, and conversion to skeleton forms. Figure 20(c) shows geometry smoothing from an optimised solution in the commercial software nTopology (nTopology 2023). GIBBON (Moerman 2018) also provides smoothing, refinement, and remeshing functionality. A disadvantage of the surface representations that conventional TO tools generate is that they are difficult to convert to an editable 3D CAD model (STEP, IGES, etc.). Recent TO research on isogeometric analysis techniques employ geometry representations such as non-uniform rational basis spline (NURBS) (Costa et al. 2021; Montemurro and Refai 2021), and T-Splines (Zhao et al. 2020b) to overcome this issue. While they show promise for simplified conversion to an editable 3D CAD model (Costa and Montemurro 2020), to our knowledge no open-source tools currently exist that can reliably do this conversion from 3D isogeometric representations.

After traditional smoothing and remeshing operations, the CAD model can be prepared further by considering MAM process modelling. Besides considering AM constraints previously discussed (e.g. feature size and supportless geometries), simulating MAM processes is a non-trivial problem that requires the coupling of models at different length scales (Francois et al. 2017; DebRoy et al. 2021; Wei et al. 2021) (see Figure 20(d) for overview of model coupling). Thorough reviews of the state of MAM process simulation are provided in Francois et al. (2017), DebRoy et al. (2021) and Wei et al. (2021), which also reference many commercial and open-source software tools. Here we refer the reader to some additional open-source tools and research conducted recently. Moran et al. (2021) developed a tool that models thermal stresses during powder bed fusion (PBF), using thermal fields to predict defect occurrences. For a sample part studied in Figure 20(e), they demonstrated that geometry, layer elevation, and scan strategy can influence defect generation, due to inadequate or excessive thermal energy (Moran et al. 2021). Also, Rodgers et al. (2021) developed the Potts Monte Carlo tool SPPARKS to simulate grain growth mechanics during PBF processing. To prepare designs for MAM fabrication, process models are ideally coupled with scan path optimisation techniques and they have been studied recently in Liu et al. (2021a), Liu et al. (2020a), and Boissier et al. (2020). To enable greater tool path control and geometric freedom, Gleadall (2021) developed a flexible path planning open-source tool. Both non-extruding and extruding paths can be controlled, and non-planar print paths, feed rates, speeds, etc. can be defined. Overall, advanced path planning and optimisation techniques can still be developed further (Zhao and Guo 2020) and coupled with AM process simulation for their effective deployment in software tools.

7.2. Commercial software

Seven different commercial TO tools that offer complete workflows (including pre- and post-processing functionalities) are compared in Table 3 based on their functionality. Desired functionalities for MAM are considered, such as functionally graded latticing, overhang, and feature size constraints. Fusion 360 (Autodesk 2022) uses a generative design tool that employs machine learning methods and cloud-based solving to enhance its TO features. While being a unique alternative to other commercial tools, it lacks some tools for enabling AM designs. Conversely, some of the tools with more AM functionality include nTopology (nTopology 2023), ANSYS Mechanical (Ansys Inc 2022), Optistruct (Altair Engineering 2021a), and Inspire (Altair Engineering 2021b). nTopology’s (nTopology 2023) unique capabilities include many lattice design tools, implicit modelling, and field-based designs. Optistruct (Altair Engineering 2021a) is one of the most-developed software tools for TO, allowing more complex multi-physics definitions and providing SIMP, RAMP, polynomial, and level-set TO methods. ANSYS Mechanical (Ansys Inc 2022) also provides similar powerful features including allowing build direction definitions, SIMP and level-set methods, and multiple solver types including sequential quadratic programming (SQP) and optimality criteria (OC). Inspire (Altair Engineering 2021b) is a more user-friendly version of Optistruct (Altair Engineering 2021a), with some of the advanced user functions removed in exchange for a simpler UI.

Table 3. Commercial TO software with multiple functionalities of interest.

Software	Version	Problem Type	MM^a	Anisotropy^a	Multi-objective^a	Lattices^a	Overhang Constraints^a	Feature Size Constraints^a
Fusion 360 Generative design (Autodesk 2022)	Student Edition	Structural					X	X
nTopology (nTopology 2023)	3.10.3	Structural			X	X	X
Optistruct (Altair Engineering 2021a)	2020	Thermal, Structural		X	X	X	X	X
Inspire (Altair Engineering 2021b)	2020	Structural			X	X	X	X
ProTOP (CAESS 2022)	6.2	Structural, Thermal			X	X		X
Abaqus Simulia (Dassault Systemes 2021)	2020	Structural		X	X			X
ANSYS Mechanical (Ansys Inc 2022)	R2021	Structural, Thermal		X	X	X	X	X

^a Functions that are available in the tool are marked with an ‘X’.

We note that while multi-material (MM) metal TO methods have been implemented in research (Bohrer and Kim 2021; Kazemi et al. 2020; Sha et al. 2021), none of the seven commercial tools here possess this functionality. Just as the advent of practical AM processes sparked renewed interest in TO (Gebisa and Lemu 2017a), we expect TO software progression to be partially dictated by AM’s technological development. Ongoing research in the field of MM MAM shows great promise for increasing design flexibility more suitable for TO. For example, Wei et al. (2019) produced parts with a MM continuous gradient between Cu10Sn and 316L stainless steel (SS) using selective laser melting. These continuous gradient designs would be well-suited to mesh-based TO, which naturally produces material gradients (Zegard and Paulino 2016) (which are normally penalised for single material optimizations). However, MM MAM parts are still only being produced in laboratory settings and require more development to reliably produce MM topology-optimised geometries (Schneck et al. 2021; Gralow et al. 2020). We expect that future demand, development, and commercialisation of MM TO tools will increase as MM MAM processes become more practical.

8. Conclusion

In this work, the symbiosis between TO and MAM has been amply examined. This investigation has covered industry-related applications, support structure designs, manufacturability-oriented designs, porous considerations, artificial intelligence-assisted modelling, and software availability. This study has shown that several advancements have been made to address future considerations suggested by Liu et al. (2018) in 2018 such as process-induced residual stress/deformation integrated into TO and combined support-free and build orientation TO. In addition to these, in the past 5 years, we have observed hundreds of research efforts go into the design or redesign of components in the aerospace, automotive, medical, and other industries using TO and MAM. There have also been model considerations for enclosed cavities and process-influenced geometrical constraints. An interesting and nascent field of study is the use of machine and deep learning approaches to either generate topology-optimised structures or realise a wider DfAM spectrum. A former major hindrance to actualising practical or working designs in DfAM is software capabilities, however, the past few years have revealed new or enhanced open-source and commercial frameworks which either consider parallel computing or utilise new modelling strategies such as implicit and field-driven concepts.

Even with the immense progress achieved in TO for MAM, there are still several boxes that need to be checked. A foremost challenge is validating and standardising the several algorithms developed such that they become widely applicable. We observe that in the industrial case studies, very few studies included the many manufacturability-constrained TO approaches. The disconnect between these algorithms and DfAM for practical use cases needs to be studied and worked upon. Artificial intelligence-assisted models need to be extended to large-scale, high-resolution TO problems while considering additive manufacturing limitations. Notwithstanding, the immense research effort being put into these areas and the promising results obtained already only affirm the prosperous future of TO for MAM as forecasted by Liu et al. (2018).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This work was supported by funding from the Natural Sciences and Engineering Research Council of Canada (NSERC), the Federal Economic Development Agency for Southern Ontario (FedDev Ontario No: 814654), and Siemens Energy Canada Limited.

Notes on contributors

Osezua Ibhadode

Dr. Osezua Ibhadode is an assistant professor in Mechanical Engineering at the University of Alberta, Edmonton, Canada, and directs the new Multifunctional Design and Additive Manufacturing lab. His research is focused on design for additive manufacturing for multiphysics and multidisciplinary applications. He obtained his Ph.D. in Mechanical Engineering and completed a postdoctoral fellowship in the Multiscale Additive Manufacturing (MSAM) lab at the University of Waterloo.

Zhidong Zhang

Dr. Zhidong Zhang is a leading researcher who specializes in the study of high-performance computing for additive manufacturing-oriented structural optimization. He received his Ph.D. in Mechanical Engineering from the University of Waterloo, Canada. His research interests include heat source modeling, structural topology optimization, and parallel computing for metal additive manufacturing. His research has been published in many academic journals and he has presented his findings at recognized conferences around the globe.

Jeffrey Sixt

Mr. Jeffrey Sixt holds a MA.Sc in Mechanical and Mechatronics Engineering from the University of Waterloo. During his degree he specialized in leveraging AM for vibration strain sensing wearable devices and developed design optimization algorithms for AM-based designs. He now works at an augmented reality startup designing light engines.

Ken M. Nsiempba

Mr. Ken M. Nsiempba holds a MA.Sc. in Mechanical and Mechatronics Engineering from the University of Waterloo. During his degree program, he focused on studying how to effectively manage the coupling of geometrical constraints in additive manufacturing within the topology optimization process. He possesses extensive expertise in computational geometry and currently serves as a data scientist at a medical startup, where he specializes in analyzing medical images.

Joseph Orakwe

Mr. Joseph Nonso Orakwe is a Ph.D. student at the University of Waterloo's Mechanical & Mechatronics Engineering department, conducting research on design optimization for additive manufacturing at the Multi-Scale Additive Manufacturing Lab (MSAM). He completed his bachelor's studies at the University of Benin, Nigeria and his Master's degree at the Technical University of Ingolstadt, Germany.

Alexander Martinez-Marchese

Dr. Alexander Martinez-Marchese obtained his Bachelor's and Master's degrees from the University of Toronto in mechanical engineering. After his master's Alexander worked as a research engineer at Dyson Technology Ltd., where he specialized in gas-particle separation technologies, experimental fluid dynamics, and CFD, and obtained an international patent on a low-energy particle separation system. Afterward, he completed a Ph.D. at the Multiscale Additive Manufacturing (MSAM) lab, University of Waterloo, where he researched laser ultrasonics, and developed and obtained a patent for a novel technology for directed energy deposition called ultrasound particle lensing. He is currently a Postdoctoral Fellow at the MSAM lab.

Osazee Ero

Mr. Osazee Ero is a Ph.D. candidate at the University of Waterloo's Mechanical & Mechatronics Engineering department, conducting research on artificial intelligence for quality assurance in additive manufacturing at the Multi-Scale Additive Manufacturing (MSAM) lab. He completed his Bachelor's studies in Electrical/Electronics Engineering at the University of Benin and his Master's degree in Systems Engineering at the University of Lagos, both in Nigeria.

Shahriar Imani Shahabad

Dr. Shahriar Imani Shahabad completed his Ph.D. at the University of Waterloo in the Multiscale Additive Manufacturing (MSAM) lab. His main research is on the multi-physics modeling of additive manufacturing processes, especially Laser Powder-bed Fusion (L-PBF) and Electron Beam Powder-bed Fusion (E-BPBF) processes. He is involved in an industrial project related to the topology optimization of fluid channels in heat exchanger components.

Ali Bonakdar

Dr. Ali Bonakdar is an Advanced Manufacturing Technology Lead at Siemens Energy Canada Limited, Gas and Power Division, responsible for the strategic development of various advanced manufacturing processes with a particular focus on additive manufacturing. In addition to his industrial role, he is an Adjunct Professor at Concordia University, University of Waterloo, Western University, and École de technologie supérieure (ÉTS); leading several industrial-academic research projects.

Ehsan Toyserkani

Dr. Ehsan Toyserkani is a professor in Mechanical and Mechatronics Engineering, at the University of Waterloo. He holds the Canada Research Chair position in Additive Manufacturing (AM) and has over 20 years of experience in different aspects of AM research and development, from mechatronics AM system development to AM applications in medicine and engineering. He established the first AM laboratory at a Canadian university - the Multi-Scale Additive Manufacturing (MSAM) Laboratory – which focuses on the development of the next generation of AM processes and applications.