Topology optimization for multi-layer multi-material composite structures

References

• Alfouneh, M., J. Ji, and Q. Luo. 2020. “Optimal Design of Multi-cellular Cores for Sandwich Panels Under Harmonic Excitation.” Composite Structures 248: 112507.
   Web of Science ®Google Scholar
• Alfouneh, M., J. Ji, and Q. Luo. 2021. “Damping Design of Harmonically Excited Flexible Structures with Graded Materials to Minimize Sound Pressure and Radiation.” Engineering Optimization 53 (2): 348–367.
   Web of Science ®Google Scholar
• Alfouneh, M., and L. Tong. 2017. “Maximizing Modal Damping in Layered Structures via Multi-objective Topology Optimization.” Engineering Structures 132: 637–647.
   Web of Science ®Google Scholar
• Allaire, G., and G. Delgado. 2016. “Stacking Sequence and Shape Optimization of Laminated Composite Plates via a Level-Set Method.” Journal of the Mechanics and Physics of Solids 97: 168–196.
   Web of Science ®Google Scholar
• Banh, T. T., and D. Lee. 2019. “Topology Optimization of Multi-Directional Variable Thickness Thin Plate with Multiple Materials.” Structural and Multidisciplinary Optimization 59 (5): 1503–1520.
   Web of Science ®Google Scholar
• Bendsøe, M. P., and O. Sigmund. 2007. “Topology Optimization.” In Optimization of Structural and Mechanical Systems, Edited By: Jasbir S Arora (University of Iowa, USA), 161–194. World Scientific.
   Google Scholar
• Bourdin, B., and A. Chambolle. 2003. “Design-Dependent Loads in Topology Optimization.” ESAIM: Control, Optimisation and Calculus of Variations 9: 19–48.
   Web of Science ®Google Scholar
• Chau, K. N., K. N. Chau, T. Ngo, K. Hackl, and H. Nguyen-Xuan. 2018. “A Polytree-Based Adaptive Polygonal Finite Element Method for Multi-material Topology Optimization.” Computer Methods in Applied Mechanics and Engineering 332: 712–739.
   Web of Science ®Google Scholar
• Chu, S., M. Xiao, L. Gao, H. Li, J. Zhang, and X. Zhang. 2019. “Topology Optimization of Multi-material Structures with Graded Interfaces.” Computer Methods in Applied Mechanics and Engineering 346: 1096–1117.
   Web of Science ®Google Scholar
• Coelho, P., J. Guedes, and H. Rodrigues. 2015. “Multiscale Topology Optimization of Bi-material Laminated Composite Structures.” Composite Structures 132: 495–505.
   Web of Science ®Google Scholar
• Cui, M., H. Chen, and J. Zhou. 2016. “A Level-Set Based Multi-material Topology Optimization Method Using a Reaction Diffusion Equation.” Computer-Aided Design 73: 41–52.
   Web of Science ®Google Scholar
• Cui, M., H. Chen, J. Zhou, and F. Wang. 2017. “A Meshless Method for Multi-material Topology Optimization Based on the Alternating Active-Phase Algorithm.” Engineering with Computers 33 (4): 871–884.
   Web of Science ®Google Scholar
• Dai, Y., M. Feng, and M. Zhao. 2017. “Topology Optimization of Laminated Composite Structures with Design-Dependent Loads.” Composite Structures 167: 251–261.
   Web of Science ®Google Scholar
• Fang, C., and G. S. Springer. 1993. “Design of Composite Laminates by a Monte Carlo Method.” Journal of Composite Materials 27 (7): 721–753.
   Web of Science ®Google Scholar
• Gadipudi, V. K. 2018. “Topology Optimization of Lightweight Structural Composites Inspired by Cuttlefish Bone.” (PhD Electronic Theses and Dissertations). South Dakota State University.
   Google Scholar
• Gan, N., and Q. Wang. 2021. “Topology Optimization of Multiphase Materials with Dynamic and Static Characteristics by BESO Method.” Advances in Engineering Software 151: 102928.
   Web of Science ®Google Scholar
• Guo, X., W. Zhang, and W. Zhong. 2014. “Doing Topology Optimization Explicitly and Geometrically—A New Moving Morphable Components Based Framework.” Journal of Applied Mechanics 81 (8): 081009.
   Web of Science ®Google Scholar
• He, M., X. Zhang, L. dos Santos Fernandez, A. Molter, L. Xia, and T. Shi. 2021. “Multi-material Topology Optimization of Piezoelectric Composite Structures for Energy Harvesting.” Composite Structures 265: 113783.
   Web of Science ®Google Scholar
• Huang, X., Y. Li, S. Zhou, and Y. Xie. 2014. “Topology Optimization of Compliant Mechanisms with Desired Structural Stiffness.” Engineering Structures 79: 13–21.
   Web of Science ®Google Scholar
• Huang, X., and Y.-M. Xie. 2010. “A Further Review of ESO Type Methods for Topology Optimization.” Structural and Multidisciplinary Optimization 41 (5): 671–683.
   Web of Science ®Google Scholar
• Jiang, D., R. Hoglund, and D. E. Smith. 2019. “Continuous Fiber Angle Topology Optimization for Polymer Composite Deposition Additive Manufacturing Applications.” Fibers 7 (2): 14.
   Web of Science ®Google Scholar
• Kang, Z., and L. Tong. 2008. “Topology Optimization-Based Distribution Design of Actuation Voltage in Static Shape Control of Plates.” Computers & Structures 86 (19-20): 1885–1893.
   Web of Science ®Google Scholar
• Kang, Z., C. Wu, Y. Luo, and M. Li. 2019. “Robust Topology Optimization of Multi-material Structures Considering Uncertain Graded Interface.” Composite Structures 208: 395–406.
   Web of Science ®Google Scholar
• Lee, J. W., J. J. Kim, and G. H. Yoon. 2019. “Stress Constraint Topology Optimization Using Layerwise Theory for Composite Laminates.” Composite Structures 226: 111184.
   Web of Science ®Google Scholar
• Lieu, Q. X., and J. Lee. 2017. “A Multi-Resolution Approach for Multi-material Topology Optimization Based on Isogeometric Analysis.” Computer Methods in Applied Mechanics and Engineering 323: 272–302.
   Web of Science ®Google Scholar
• Liu, P., Y. Luo, and Z. Kang. 2016. “Multi-material Topology Optimization Considering Interface Behavior via XFEM and Level Set Method.” Computer Methods in Applied Mechanics and Engineering 308: 113–133.
   Web of Science ®Google Scholar
• Luo, X., E. Li, and H. Wang. 2021. “A Surrogate Assisted Thermal Optimization Framework for Design of Pin-Fin Heat Sink for the Platform Inertial Navigation System.” Engineering Optimization 53 (1): 145–164.
   Web of Science ®Google Scholar
• Luo, Z., Q. Luo, L. Tong, W. Gao, and C. Song. 2011. “Shape Morphing of Laminated Composite Structures with Photostrictive Actuators Via Topology Optimization.” Composite Structures 93 (2): 406–418.
   Web of Science ®Google Scholar
• Luo, Q., and L. Tong. 2015. “Design and Testing for Shape Control of Piezoelectric Structures Using Topology Optimization.” Engineering Structures 97: 90–104.
   Web of Science ®Google Scholar
• Luo, Q., and L. Tong. 2017. “A Deformation Mechanism Based Material Model for Topology Optimization of Laminated Composite Plates and Shells.” Composite Structures 159: 246–256.
   Web of Science ®Google Scholar
• Maute, K., A. Tkachuk, J. Wu, H. Jerry Qi, Z. Ding, and M. L. Dunn. 2015. “Level Set Topology Optimization of Printed Active Composites.” Journal of Mechanical Design 137 (11): 111402.
   PubMed Web of Science ®Google Scholar
• Otomori, M., T. Yamada, K. Izui, and S. Nishiwaki. 2015. “Matlab Code for a Level Set-Based Topology Optimization Method Using a Reaction Diffusion Equation.” Structural and Multidisciplinary Optimization 51 (5): 1159–1172.
   Web of Science ®Google Scholar
• Park, J., and A. Sutradhar. 2015. “A Multi-resolution Method for 3D Multi-material Topology Optimization.” Computer Methods in Applied Mechanics and Engineering 285: 571–586.
   Web of Science ®Google Scholar
• Rupp, C. J., A. Evgrafov, K. Maute, and M. L. Dunn. 2009. “Design of Piezoelectric Energy Harvesting Systems: A Topology Optimization Approach Based on Multilayer Plates and Shells.” Journal of Intelligent Material Systems and Structures 20 (16): 1923–1939.
   Web of Science ®Google Scholar
• Salas, R. A., F. J. Ramírez-Gil, W. Montealegre-Rubio, E. C. N. Silva, and J. N. Reddy. 2018. “Optimized Dynamic Design of Laminated Piezocomposite Multi-entry Actuators Considering Fiber Orientation.” Computer Methods in Applied Mechanics and Engineering 335: 223–254.
   Web of Science ®Google Scholar
• Sanders, E. D., A. Pereira, M. A. Aguiló, and G. H. Paulino. 2018. “PolyMat: An Efficient Matlab Code for Multi-material Topology Optimization.” Structural and Multidisciplinary Optimization 58 (6): 2727–2759.
   Web of Science ®Google Scholar
• Shimoda, M., H. Nakayama, S. Suzaki, and R. Tsutsumi. 2021. “A Unified Simultaneous Shape and Topology Optimization Method for Multi-material Laminated Shell Structures.” Structural and Multidisciplinary Optimization 64 (6): 3569–3604.
   Web of Science ®Google Scholar
• Sliseris, J., and K. Rocens. 2013. “Optimal Design of Composite Plates with Discrete Variable Stiffness.” Composite Structures 98: 15–23.
   Web of Science ®Google Scholar
• Stolarski, T., Y. Nakasone, and S. Yoshimoto. 2018. Engineering Analysis with ANSYS Software. Butterworth-Heinemann The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom. 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States.
   Google Scholar
• Sun, Z., D. Li, W. Zhang, S. Shi, and X. Guo. 2017. “Topological Optimization of Biomimetic Sandwich Structures with Hybrid Core and CFRP Face Sheets.” Composites Science and Technology 142: 79–90.
   Web of Science ®Google Scholar
• Sun, X., J. Yang, Y. Xie, X. Huang, and Z. Zuo. 2011. “Topology Optimization of Composite Structure Using Bi-directional Evolutionary Structural Optimization Method.” Procedia Engineering 14: 2980–2985.
   Google Scholar
• Tang, Y., A. Kurtz, and Y. F. Zhao. 2015. “Bidirectional Evolutionary Structural Optimization (BESO) Based Design Method for Lattice Structure to be Fabricated by Additive Manufacturing.” Computer-Aided Design 69: 91–101.
   Web of Science ®Google Scholar
• Tavakoli, R., and S. M. Mohseni. 2014. “Alternating Active-Phase Algorithm for Multimaterial Topology Optimization Problems: A 115-Line MATLAB Implementation.” Structural and Multidisciplinary Optimization 49 (4): 621–642.
   Web of Science ®Google Scholar
• Tong, X., W. Ge, Y. Zhang, and Z. Zhao. 2019. “Topology Design and Analysis of Compliant Mechanisms with Composite Laminated Plates.” Journal of Mechanical Science and Technology 33 (2): 613–620.
   Web of Science ®Google Scholar
• Tong, L., and J. Lin. 2011. “Structural Topology Optimization with Implicit Design Variable—Optimality and Algorithm.” Finite Elements in Analysis and Design 47 (8): 922–932.
   Web of Science ®Google Scholar
• Tong, L., and Q. Luo. 2016. “Design of Cellular Structures with Multi-volume Fractions Using Topology Optimization.” Jisuan Lixue Xuebao/Chinese Journal of Computational Mechanics 33 (4): 516–521.
   Google Scholar
• Vasista, S., and L. Tong. 2012. “Design and Testing of Pressurized Cellular Planar Morphing Structures.” AIAA Journal 50 (6): 1328–1338.
   Web of Science ®Google Scholar
• Wang, Y., Z. Luo, Z. Kang, and N. Zhang. 2015. “A Multi-Material Level Set-Based Topology and Shape Optimization Method.” Computer Methods in Applied Mechanics and Engineering 283: 1570–1586.
   Web of Science ®Google Scholar
• Wang, M. Y., X. Wang, and D. Guo. 2003. “A Level Set Method for Structural Topology Optimization.” Computer Methods in Applied Mechanics and Engineering 192 (1-2): 227–246.
   Web of Science ®Google Scholar
• Wang, M. Y., and S. Zhou. 2004. “Synthesis of Shape and Topology of Multi-material Structures with a Phase-Field Method.” Journal of Computer-Aided Materials Design 11 (2-3): 117–138.
   Google Scholar
• Zhang, X. S., H. Chi, and G. H. Paulino. 2020. “Adaptive Multi-material Topology Optimization with Hyperelastic Materials Under Large Deformations: A Virtual Element Approach.” Computer Methods in Applied Mechanics and Engineering 370: 112976.
   Web of Science ®Google Scholar
• Zhang, H., X. Ding, H. Li, and M. Xiong. 2019. “Multi-scale Structural Topology Optimization of Free-Layer Damping Structures with Damping Composite Materials.” Composite Structures 212: 609–624.
   Web of Science ®Google Scholar
• Zhang, X. S., G. H. Paulino, and A. S. Ramos. 2018. “Multi-material Topology Optimization with Multiple Volume Constraints: A General Approach Applied to Ground Structures with Material Nonlinearity.” Structural and Multidisciplinary Optimization 57 (1): 161–182.
   Web of Science ®Google Scholar
• Zhang, W., J. Song, J. Zhou, Z. Du, Y. Zhu, Z. Sun, and X. Guo. 2018. “Topology Optimization with Multiple Materials Via Moving Morphable Component (MMC) Method.” International Journal for Numerical Methods in Engineering 113 (11): 1653–1675.
   Web of Science ®Google Scholar
• Zhang, J., S. Wang, H. Zhou, and L. Ning. 2021. “Multi-component Topology Optimization for Thin-Walled Structures.” Engineering Optimization, 1–17. doi:10.1080/0305215X.2021.1901283.
   Web of Science ®Google Scholar
• Zhao, Z., and X. S. Zhang. 2021. “Design of Graded Porous Bone-Like Structures Via a Multi-material Topology Optimization Approach.” Structural and Multidisciplinary Optimization 64 (2): 677–698.
   Web of Science ®Google Scholar
• Zhou, S., and M. Y. Wang. 2007. “Multimaterial Structural Topology Optimization with a Generalized Cahn–Hilliard Model of Multiphase Transition.” Structural and Multidisciplinary Optimization 33 (2): 89–111.
   Web of Science ®Google Scholar
• Zuo, W., and K. Saitou. 2017. “Multi-material Topology Optimization Using Ordered SIMP Interpolation.” Structural and Multidisciplinary Optimization 55 (2): 477–491.
   Web of Science ®Google Scholar