Integrated optimization of the material and structure of composites based on the Heaviside penalization of discrete material model

详细信息    查看全文

• 作者：Zunyi Duan (1)
  Jun Yan (1)
  Guozhong Zhao (1)
  
  1. Department of Engineering Mechanics ; State Key Laboratory for Structural Analysis of Industrial Equipment ; Dalian University of Technology ; 116023 ; Dalian ; China
  
• 关键词：Composite material ; Discrete material optimization ; Heaviside Penalization ; Integrated optimization of material and structure
• 刊名：Structural and Multidisciplinary Optimization
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：51
• 期：3
• 页码：721-732
• 全文大小：1,910 KB
• 参考文献：1. Banichuk, NV, Karihaloo, BL (1976) Minimum-weight design of multipurpose cylindrical bars. Int J Solids Struct 12: pp. 267-273 CrossRef
  2. Bendsoe, MP, Kikuchi, N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71: pp. 197-224 CrossRef
  3. Bendsoe, M, Sigmund, O (2003) Topology optimization-theory, methods and applications. Springer, Berlin
  4. Bruyneel, M (2011) SFP-a new parameterization based on shape functions for optimal material selection: application to conventional composite plies. Struct Multidiscip Optim 43: pp. 17-27 CrossRef
  5. Callahan, KJ, Weeks, GE (1992) Optimum design of composite laminates using genetic algorithms. Compos Eng 2: pp. 149-160 CrossRef
  6. Deaton, JD, Grandhi, RV (2014) A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct Multidiscip Optim 49: pp. 1-38 CrossRef
  7. Eschenauer, HA, Olhoff, N (2001) Topology optimization of continuum structures a review. Am Soc Mech Eng 54: pp. 331-390
  8. Ferreira HTL, Rodrigues HC, Guedes JM, Hernandes JA (2013) Hierarchical optimization of laminated fiber reinforced composites. In: Proceedings of 10th word congress on structural and multidisciplinary optimization Orlando, Florida, USA, May 19鈥?4
  9. Froes, FH, Suryanarayana, C, Eliezer, D (1992) Synthesis, properties and applications of titanium aluminides. J Mater Sci 27: pp. 5113-5140 CrossRef
  10. Gao, T, Zhang, W (2011) A mass constraint formulation for structural topology optimization with multiphase materials[J]. Int J Numer Methods Eng 88: pp. 774-796 CrossRef
  11. Gao, T, Zhang, W, Duysinx, P (2012) A bi-value coding parameterization scheme for the discrete optimal orientation design of the composite laminate. Int J Numer Methods Eng 91: pp. 98-114 CrossRef
  12. Graesser, DL, Zabinsky, ZB, Tuttle, ME, Kim, GI (1991) Designing laminated composites using random search techniques. Compos Struct 18: pp. 311-325 CrossRef
  13. Guest, JK (2009) Imposing maximum length scale in topology optimization. Struct Multidiscip Optim 37: pp. 463-473 CrossRef
  14. Guest, JK, Prevost, JH, Belytschko, T (2004) Achieving minimum length scale in topology optimization using nodal design variables and projection functions. Int J Numer Methods Eng 61: pp. 238-254 CrossRef
  15. Guest, JK, Asadpoure, A, Ha, SH (2011) Eliminating beta-continuation from Heaviside projection and density filter algorithms. Struct Multidiscip Optim 44: pp. 443-453 CrossRef
  16. Hao, Z (2002) Applications and prospects of magnesium and its alloys in aerospace. Aviat Eng Maint 04: pp. 41-42
  17. Hvejsel, CF, Lund, E (2011) Material interpolation schemes for unified topology and multi-material optimization. Struct Multidiscip Optim 43: pp. 811-825 CrossRef
  18. Lund, E (2009) Buckling topology optimization of laminated multi-material composite shell structures. Compos Struct 91: pp. 158-167 CrossRef
  19. Lund, E, Stegmann, J (2005) On structural optimization of composite shell structures using a discrete constitutive parametrization. Wind Energy 8: pp. 109-124 CrossRef
  20. Nagendra, S, Jestin, D, Gurdal, Z, Haftka, RT, Watson, LT (1996) Improved genetic algorithm for the design of stiffened composite panels. Comput Struct 58: pp. 543-555 CrossRef
  21. Niu, B, Olhoff, N, Lund, E, Cheng, G (2010) Discrete material optimization of vibrating laminated composite plates for minimum sound radiation. Int J Solids Struct 47: pp. 2097-2114 CrossRef
  22. Park, JH, Hwang, JH, Lee, CS, Hwang, W (2001) Stacking sequence design of composite laminates for maximum strength using genetic algorithms. Compos Struct 52: pp. 217-231 CrossRef
  23. Pelletier, JL, Vel, SS (2006) Multi-objective optimization of fiber reinforced composite laminates for strength, stiffness and minimal mass. Comput Struct 84: pp. 2065-2080 CrossRef
  24. Powell, MJD (1978) Algorithms for non-linear constraints that use lagrangian functions. Math Program 14: pp. 224-248 CrossRef
  25. Rozvany, GIN, Zhou, M, Birker, T (1992) Generalized shape optimization without homogenization. Struct Optim 4: pp. 250-252 CrossRef
  26. Du, S (2007) Advanced composite materials and aerospace engineering. Acta Mater Compositae Sin 1: pp. 1-12
  27. Sigmund, O (2007) Morphology-based black and white filters for topology optimization. Struct Multidiscip Optim 33: pp. 401-424 CrossRef
  28. Sigmund O, Maute K (2013) Topology optimization approaches. Struct Multidiscip Optim 1鈥?5
  29. Stegmann, J, Lund, E (2005) Discrete material optimization of general composite shell structures. Int J Numer Methods Eng 62: pp. 2009-2027 CrossRef
  30. Weck, M, Steinke, P (1983) An efficient technique in shape optimization. J Struct Mech 11: pp. 433-449 CrossRef
  31. Xu, S, Cai, Y, Cheng, G (2010) Volume preserving nonlinear density filter based on Heaviside functions. Struct Multidiscip Optim 41: pp. 495-505 CrossRef
  
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Computer-Aided Engineering and Design
  Numerical and Computational Methods in Engineering
  Engineering Design
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1615-1488

文摘

Based on discrete material optimization and topology optimization technologies, this paper discusses the problem of integrated optimization design of the material and structure of fiber-reinforced composites by considering the characteristics of the discrete variable of fiber ply angle because of the manufacture requirements. An optimization model based on the minimum structural compliance with a specified composite volume constraint is established. The ply angle and the distribution of the composite material are introduced as independent variables in two geometric scales (material and structural scales). The void material is added into the optional discrete material set to realize the topology change of the structure. This paper proposes an improved HPDMO (Heaviside Penalization of Discrete Material Optimization) model to obtain a better convergent result, and an explicit sensitivity analysis is performed. The effects of the HPDMO model on the convergence rate of the optimization results, the objective function value and the iteration history are studied and compared with those from the classical Discrete Material Optimization model and the Continuous Discrete Material Optimization model in this paper. Numerical examples in this paper show that the HPDMO model can effectively achieve the integrated optimization of the fiber ply angle and its distribution in the structural domain, and can also considerably improve the convergence rate of the optimal results compared with other DMO models. This model will help to reduce the manufacture cost of the optimal design.