A novel design strategy to enhance buckling resistance of thin-walled single-cell lattice structures via topology optimisation

References

• Ashby MF, Medalist RFM. The mechanical properties of cellular solids. Metall Trans A. Sep. 1983;14(9):1755–1769. doi:10.1007/BF02645546
   Web of Science ®Google Scholar
• Nazir A, Abate KM, Kumar A, et al. A state-of-the-art review on types, design, optimization, and additive manufacturing of cellular structures. Int J Adv Manuf Technol. Oct. 2019;104(9):3489–3510. doi:10.1007/s00170-019-04085-3
   Web of Science ®Google Scholar
• Nazir A, Jeng J-Y. Buckling behavior of additively manufactured cellular columns: experimental and simulation validation. Mater Des. Jan. 2020;186:108349. doi:10.1016/j.matdes.2019.108349
   Web of Science ®Google Scholar
• Eremeyev VA, Turco E. Enriched buckling for beam-lattice metamaterials. Mech Res Commun. Jan. 2020;103:103458. doi:10.1016/j.mechrescom.2019.103458
   Web of Science ®Google Scholar
• He Y, Zhou Y, Liu Z, et al. Buckling and pattern transformation of modified periodic lattice structures. Extreme Mech Lett. Jul. 2018;22:112–121. doi:10.1016/j.eml.2018.05.011
   Web of Science ®Google Scholar
• Manickarajah D, Xie YM, Steven GP. Optimisation of columns and frames against buckling. Comput Struct. Mar. 2000;75(1):45–54. doi:10.1016/S0045-7949(99)00082-6
   Web of Science ®Google Scholar
• Bertoldi K. Harnessing instabilities to design tunable architected cellular materials. Annu Rev Mater Res. 2017;47(1):51–61. doi:10.1146/annurev-matsci-070616-123908
   Google Scholar
• Viswanath A, Khalil M, Al Maskari F, et al. Harnessing buckling response to design lattice structures with improved buckling strength. Mater Des. Aug. 2023;232:112113. doi:10.1016/j.matdes.2023.112113
   Web of Science ®Google Scholar
• Bendsøe MP, Triantafyllidis N. Scale effects in the optimal design of a microstructured medium against buckling. Int J Solids Struct. Jan. 1990;26(7):725–741. doi:10.1016/0020-7683(90)90003-E
   Web of Science ®Google Scholar
• Neves MM, Rodrigues H, Guedes JM. Generalized topology design of structures with a buckling load criterion. Struct Optim. Oct. 1995;10(2):71–78. doi:10.1007/BF01743533
   Google Scholar
• Mitjana F, Cafieri S, Bugarin F, et al. Topological gradient in structural optimization under stress and buckling constraints. Appl Math Comput. Nov. 2021;409:126032. doi:10.1016/j.amc.2021.126032
   Web of Science ®Google Scholar
• Gao X, Li L, Ma H. An adaptive continuation method for topology optimization of continuum structures considering buckling constraints. Int J Appl Mechanics. Oct. 2017;9(7):1750092. doi:10.1142/S1758825117500922
   Web of Science ®Google Scholar
• Gao X, Ma H. Topology optimization of continuum structures under buckling constraints. Comput Struct. Sep. 2015;157:142–152. doi:10.1016/j.compstruc.2015.05.020
   Web of Science ®Google Scholar
• Sekimoto T, Noguchi H. Homologous topology optimization in large displacement and buckling problems. JSME Int J Solid Mech Mater Eng. 2001;44(4):616–622. doi:10.1299/jsmea.44.616
   Web of Science ®Google Scholar
• Bruns TE, Sigmund O. Toward the topology design of mechanisms that exhibit snap-through behavior. Comput Methods Appl Mech Eng. Sep. 2004;193(36):3973–4000. doi:10.1016/j.cma.2004.02.017
   Web of Science ®Google Scholar
• Kemmler R, Lipka A, Ramm E. Large deformations and stability in topology optimization. Struct Multidisc Optim. Dec. 2005;30(6):459–476. doi:10.1007/s00158-005-0534-0
   Web of Science ®Google Scholar
• Bian X, Fang Z. Large-scale buckling-constrained topology optimization based on assembly-free finite element analysis. Adv Mech Eng. Sep. 2017;9(9):1687814017715422. doi:10.1177/1687814017715422
   Web of Science ®Google Scholar
• Xu T, Lin X, Xie YM. Bi-directional evolutionary structural optimization with buckling constraints. Struct Multidisc Optim. Mar. 2023;66(4):67. doi:10.1007/s00158-023-03517-9
   Web of Science ®Google Scholar
• Neves MM, Sigmund O, Bendsøe MP. Topology optimization of periodic microstructures with a penalization of highly localized buckling modes. Int J Numer Methods Eng. Jun. 2002;54(6):809–834. doi:10.1002/nme.449
   Web of Science ®Google Scholar
• Thomsen CR, Wang F, Sigmund O. Buckling strength topology optimization of 2D periodic materials based on linearized bifurcation analysis. Comput Methods Appl Mech Eng. Sep. 2018;339:115–136. doi:10.1016/j.cma.2018.04.031
   Web of Science ®Google Scholar
• Wang F, Sigmund O. 3D architected isotropic materials with tunable stiffness and buckling strength. J Mech Phys Solids. Jul. 2021;152:104415. doi:10.1016/j.jmps.2021.104415
   Web of Science ®Google Scholar
• Bluhm GL, Christensen K, Poulios K, et al. Experimental verification of a novel hierarchical lattice material with superior buckling strength. APL Mater. Sep. 2022;10(9):090701. doi:10.1063/5.0101390
   Web of Science ®Google Scholar
• Lindgaard E, Lund E. Nonlinear buckling optimization of composite structures. Comput Methods Appl Mech Eng. Aug. 2010;199(37):2319–2330. doi:10.1016/j.cma.2010.02.005
   Web of Science ®Google Scholar
• Lindgaard E, Lund E, Rasmussen K. Nonlinear buckling optimization of composite structures considering ‘worst’ shape imperfections. Int J Solids Struct. Nov. 2010;47(22):3186–3202. doi:10.1016/j.ijsolstr.2010.07.020
   Web of Science ®Google Scholar
• Luo Q, Tong L. Structural topology optimization for maximum linear buckling loads by using a moving iso-surface threshold method. Struct Multidisc Optim. Jul. 2015;52(1):71–90. doi:10.1007/s00158-015-1286-0
   Web of Science ®Google Scholar
• Wang Y, Sigmund O. Multi-material topology optimization for maximizing structural stability under thermo-mechanical loading. Comput Methods Appl Mech Eng. Mar. 2023;407:115938. doi:10.1016/j.cma.2023.115938
   Web of Science ®Google Scholar
• Ferrari F, Sigmund O, Guest JK. Topology optimization with linearized buckling criteria in 250 lines of Matlab. Struct Multidisc Optim. Jun. 2021;63(6):3045–3066. doi:10.1007/s00158-021-02854-x
   Web of Science ®Google Scholar
• Gibson I, Rosen D, Stucker B, et al. Design for additive manufacturing. In: Gibson I, Rosen D, Stucker B, et al., editors. Additive manufacturing technologies. Cham: Springer International Publishing; 2021. p. 555–607. doi:10.1007/978-3-030-56127-7_19
   Google Scholar
• Ibhadode O, Zhang Z, Sixt J, et al. Topology optimization for metal additive manufacturing: current trends, challenges, and future outlook. Virtual Phys Prototyp. Dec. 2023;18(1):e2181192. doi:10.1080/17452759.2023.2181192
   Web of Science ®Google Scholar
• Adam GAO, Zimmer D. On design for additive manufacturing: evaluating geometrical limitations. Rapid Prototyp J. Jan. 2015;21(6):662–670. doi:10.1108/RPJ-06-2013-0060
   Web of Science ®Google Scholar
• Mohan SR, Simhambhatla S. Adopting feature resolution and material distribution constraints into topology optimisation of additive manufacturing components. Virtual Phys Prototyp. Jan. 2019;14(1):79–91. doi:10.1080/17452759.2018.1501275
   Web of Science ®Google Scholar
• Bayat M, Zinovieva O, Ferrari F, et al. Holistic computational design within additive manufacturing through topology optimization combined with multiphysics multi-scale materials and process modelling. Prog Mater Sci. Sep. 2023;138:101129. doi:10.1016/j.pmatsci.2023.101129
   Web of Science ®Google Scholar
• Ferrari F, Sigmund O. A new generation 99 line Matlab code for compliance topology optimization and its extension to 3D. Struct Multidiscipl Optim. Oct. 2020;62(4):2211–2228. doi:10.1007/s00158-020-02629-w
   Web of Science ®Google Scholar
• Wang F, Lazarov BS, Sigmund O. On projection methods, convergence and robust formulations in topology optimization. Struct Multidisc Optim. Jun. 2011;43(6):767–784. doi:10.1007/s00158-010-0602-y
   Web of Science ®Google Scholar
• Zienkiewicz OC, Taylor RL, Fox D, editors. The finite element method for solid and structural mechanics. 7th ed. Oxford: Butterworth-Heinemann; 2014. p. i. doi:10.1016/B978-1-85617-634-7.00016-8
   Google Scholar
• Kreisselmeier G, Steinhauser R. Systematic control design by optimizing a vector performance index. In: Cuenod MA, editor. Computer aided design of control systems. Oxford: Pergamon; 1980. p. 113–117. doi:10.1016/B978-0-08-024488-4.50022-X
   Google Scholar
• 14:00–17:00. ISO/ASTM 52900:2021. ISO [Internet]. [cited 2024 Feb. 22]. Available from: https://www.iso.org/standard/74514.html
   Google Scholar
• Huang J, Chen Q, Jiang H, et al. A survey of design methods for material extrusion polymer 3D printing. Virtual Phys Prototyp. Apr. 2020;15(2):148–162. doi:10.1080/17452759.2019.1708027
   Web of Science ®Google Scholar
• Zhang L, Feih S, Daynes S, et al. Buckling optimization of Kagome lattice cores with free-form trusses. Mater Des. May 2018;145:144–155. doi:10.1016/j.matdes.2018.02.026
   Web of Science ®Google Scholar
• Hübner D, Wein F, Stingl M. Two-scale optimization of graded lattice structures respecting buckling on micro- and macroscale. Struct Multidisc Optim. Jun. 2023;66(7):163. doi:10.1007/s00158-023-03619-4
   Web of Science ®Google Scholar
• Ferrari F, Sigmund O. Towards solving large-scale topology optimization problems with buckling constraints at the cost of linear analyses. Comput Methods Appl Mech Eng. May 2020;363:112911. doi:10.1016/j.cma.2020.112911
   Web of Science ®Google Scholar
• Dunning PD, Ovtchinnikov E, Scott J, et al. Level-set topology optimization with many linear buckling constraints using an efficient and robust eigensolver. Int J Numer Methods Eng. 2016;107(12):1029–1053. doi:10.1002/nme.5203
   Web of Science ®Google Scholar
• Li S, Liao X, Lu Y, et al. A parallel structured banded DC algorithm for symmetric eigenvalue problems. CCF Trans HPC. Jun. 2023;5(2):116–128. doi:10.1007/s42514-022-00117-9
   Google Scholar