Concurrent topology optimization of structures and orientation of anisotropic materials

References

• Barile, C., C. Casavola, and F. De Cillis. 2019. “Mechanical Comparison of New Composite Materials for Aerospace Applications.” Composites Part B: Engineering 162: 122–128. doi: 10.1016/j.compositesb.2018.10.101
   Web of Science ®Google Scholar
• Blasques, J. P., and M. Stolpe. 2011. “Maximum Stiffness and Minimum Weight Optimization of Laminated Composite Beams Using Continuous Fiber Angles.” Structural and Multidisciplinary Optimization 43 (4): 573–588. doi: 10.1007/s00158-010-0592-9
   Web of Science ®Google Scholar
• Cheng, H. C., N. Kikuchi, and Z. D. Ma. 1994. “An Improved Approach for Determining the Optimal Orientation of Orthotropic Material.” Structural Optimization 8 (2-3): 101–112. doi: 10.1007/BF01743305
   Web of Science ®Google Scholar
• Danek, T., M. Kochetov, and M. A. Slawinski. 2013. “Uncertainty Analysis of Effective Elasticity Tensors Using Quaternion-Based Global Optimization and Monte-Carlo Method.” The Quarterly Journal of Mechanics and Applied Mathematics 66 (2): 253–272. doi: 10.1093/qjmam/hbt004
   Web of Science ®Google Scholar
• De Vivo Nicoloso, L. 2018. “Optimization of Varying Orientation of Continuous Fiber Direction and Its Applications to New Methods of Additive Manufacturing.” Research & Development in Material Science 3 (2), RDMS.000559.
   Google Scholar
• Díaz, A. R., and M. P. Bendsøe. 1992. “Shape Optimization of Structures for Multiple Loading Conditions Using a Homogenization Method.” Structural Optimization 4 (1): 17–22. doi: 10.1007/BF01894077
   Google Scholar
• Esposito, L., A. Cutolo, M. Barile, L. Lecce, G. Mensitieri, E. Sacco, and M. Fraldi. 2019. “Topology Optimization-Guided Stiffening of Composites Realized through Automated Fiber Placement.” Composites Part B: Engineering 164: 309–323. doi: 10.1016/j.compositesb.2018.11.032
   Web of Science ®Google Scholar
• Gao, X. J., and H. T. Ma. 2015. “A Modified Model for Concurrent Topology Optimization of Structures and Materials.” Acta Mechanica Sinica 31 (6): 890–898. doi: 10.1007/s10409-015-0502-x
   Web of Science ®Google Scholar
• Gea, H. C., and J. H. Luo. 2004. “On the Stress-Based and Strain-Based Methods for Predicting Optimal Orientation of Orthotropic Materials.” Structural and Multidisciplinary Optimization 26: 229–234. doi: 10.1007/s00158-003-0348-x
   Web of Science ®Google Scholar
• González, C., J. J. Vilatela, J. M. Molina-Aldareguía, C. S. Lopes, and J. LLorca. 2017. “Structural Composites for Multifunctional Applications: Current Challenges and Future Trends.” Progress in Materials Science 89: 194–251. doi: 10.1016/j.pmatsci.2017.04.005
   Web of Science ®Google Scholar
• Hassani, B., and E. Hinton. 1998. “A Review of Homogenization and Topology Optimization III—Topology Optimization Using Optimality Criteria.” Computers and Structures 69: 739–756. doi: 10.1016/S0045-7949(98)00133-3
   Web of Science ®Google Scholar
• Huang, X., and Y. M. Xie. 2007. “Convergent and Mesh-Independent Solutions for the Bidirectional Evolutionary Structural Optimization Method.” Finite Elements in Analysis and Design 43 (14): 1039–1049. doi: 10.1016/j.finel.2007.06.006
   Web of Science ®Google Scholar
• Huang, X., and Y. M. Xie. 2010a. Evolutionary Topology Optimization of Continuum Structures: Methods and Applications. Chichester: John Wiley & Sons.
   Google Scholar
• Huang, X., and Y. M. Xie. 2010b. “A Further Review of ESO Type Methods for Topology Optimization.” Structural and Multidisciplinary Optimization 41: 671–683. doi: 10.1007/s00158-010-0487-9
   Web of Science ®Google Scholar
• Kiyono, C. Y., E. C. N. Silva, and J. N. Reddy. 2017. “A Novel Fiber Optimization Method Based on Normal Distribution Function with Continuously Varying Fiber Path.” Composite Structures 160: 503–515. doi: 10.1016/j.compstruct.2016.10.064
   Web of Science ®Google Scholar
• Lee, J., D. Kim, T. Nomura, E. M. Dede, and J. Yoo. 2018. “Topology Optimization for Continuous and Discrete Orientation Design of Functionally Graded Fiber-Reinforced Composite Structures.” Composite Structures 201: 217–233. doi: 10.1016/j.compstruct.2018.06.020
   Web of Science ®Google Scholar
• Li, S., and S. N. Atluri. 2008. “The MLPG Mixed Collocation Method for Material Orientation and Topology Optimization of Anisotropic Solids and Structures.” Computer Modeling in Engineering and Sciences 30 (1): 37–56.
   Web of Science ®Google Scholar
• Luo, J. H., and H. C. Gea. 1998. “Optimal Orientation of Orthotropic Materials Using an Energy Based Method.” Structural Optimization 15: 230–236. doi: 10.1007/BF01203536
   Web of Science ®Google Scholar
• Majak, J., and M. Pohlak. 2010. “Optimal Material Orientation of Linear and Non-Linear Elastic 3D Anisotropic Materials.” Meccanica 45 (5): 671–680. doi: 10.1007/s11012-009-9262-7
   Web of Science ®Google Scholar
• Nomura, T., E. M. Dede, J. Lee, S. Yamasaki, T. Matsumori, A. Kawamoto, and N. Kikuchi. 2015. “General Topology Optimization Method with Continuous and Discrete Orientation Design Using Isoparametric Projection.” International Journal for Numerical Methods in Engineering 101 (8): 571–605. doi: 10.1002/nme.4799
   Web of Science ®Google Scholar
• Norris, A. N. 2006. “Optimal Orientation of Anisotropic Solids.” The Quarterly Journal of Mechanics and Applied Mathematics 59 (1): 29–53. doi: 10.1093/qjmam/hbi030
   Web of Science ®Google Scholar
• Pedersen, P. 1989. “On Optimal Orientation of Orthotropic Materials.” Structural Optimization 1 (2): 101–106. doi: 10.1007/BF01637666
   Google Scholar
• Petrovic, M., T. Nomura, T. Yamada, K. Izui, and S. Nishiwaki. 2018. “Orthotropic Material Orientation Optimization Method in Composite Laminates.” Structural and Multidisciplinary Optimization 57 (2): 815–828. doi: 10.1007/s00158-017-1777-2
   Web of Science ®Google Scholar
• Rettenwander, T., M. Fischlschweiger, and G. Steinbichler. 2014. “Computational Structural Tailoring of Continuous Fibre Reinforced Polymer Matrix Composites by Hybridisation of Principal Stress and Thickness Optimisation.” Composite Structures 108: 711–719. doi: 10.1016/j.compstruct.2013.09.063
   Web of Science ®Google Scholar
• Safonov, A. A. 2019. “3D Topology Optimization of Continuous Fiber-Reinforced Structures via Natural Evolution Method.” Composite Structures 215: 289–297. doi: 10.1016/j.compstruct.2019.02.063
   Web of Science ®Google Scholar
• Salas, R. A., F. J. Ramírez-Gil, W. Montealegre-Rubio, E. C. N. Silva, and J. N. Reddyc. 2018. “Optimized Dynamic Design of Laminated Piezocomposite Multi-entry Actuators Considering Fiber Orientation.” Computer Methods in Applied Mechanics and Engineering 335: 223–254. doi: 10.1016/j.cma.2018.02.011
   Web of Science ®Google Scholar
• Setoodeh, S., M. M. Abdalla, and Z. Gürdal. 2005. “Combined Topology and Fiber Path Design of Composite Layers Using Cellular Automata.” Structural and Multidisciplinary Optimization 30 (6): 413–421. doi: 10.1007/s00158-005-0528-y
   Web of Science ®Google Scholar
• Takezawa, A., X. P. Zhang, and Y. Koizumi. 2019. “Numerical Study on the Effective Stiffness of Topology-Optimized Lattice Structures Made of Orthotropic Crystal Grains with Optimal Orientation.” Computational Materials Science 159: 202–209. doi: 10.1016/j.commatsci.2018.12.016
   Web of Science ®Google Scholar
• Völkl, H., D. Klein, M. Franz, and S. Wartzack. 2018. “An Efficient Bionic Topology Optimization Method for Transversely Isotropic Materials.” Composite Structures 204: 359–367. doi: 10.1016/j.compstruct.2018.07.079
   Web of Science ®Google Scholar
• Xie, Y. M., and G. P. Steven. 1993. “A Simple Evolutionary Procedure for Structural Optimization.” Computers & Structures 49: 885–896. doi: 10.1016/0045-7949(93)90035-C
   Web of Science ®Google Scholar
• Yan, X., X. Huang, Y. Zha, and Y. M. Xie. 2014. “Concurrent Topology Optimization of Structures and Their Composite Microstructures.” Computers and Structures 133: 103–110. doi: 10.1016/j.compstruc.2013.12.001
   Web of Science ®Google Scholar
• Zhou, Y. Q., T. Nomura, and K. Saitou. 2018. “Multi-component Topology and Material Orientation Design of Composite Structures (MTO-C).” Computer Methods in Applied Mechanics and Engineering 342: 438–457. doi: 10.1016/j.cma.2018.07.039
   Web of Science ®Google Scholar
• Zhu, Y., J. Liu, L. Dong, H. Xu, C. Yan, B. Huang, and D. Hui. 2017. “Fiber Path Optimization Based on a Family of Curves in Composite Laminate with a Center Hole.” Composites Part B: Engineering 111: 91–102. doi: 10.1016/j.compositesb.2016.11.051
   Web of Science ®Google Scholar