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Topology design of material layout in structured composites of high stiffness and strength

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Abstract

General continuous topology design formulations based on families of classical Voigt and Reuss mixing assumptions are developed and applied to solve the multiple material layout problem for the design of high stiffness/high strength composites. In the novel design framework, computational homogenization is employed to compute stiffness and strength characteristics of individual composite designs. Alternative design formulations for both high stiffness and high strength are investigated along with design sensitivity analysis algorithms. Demonstrative material design problems for boron-epoxy and graphite-epoxy composites are solved with robust sequential quadratic programming (SQP) techniques.

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References

  • Agarwal, B.; Broutman, L. 1990:Analysis and performance of fiber composites. New York: Wiley-Interscience.

    Google Scholar 

  • Allaire, G.; Kohn, R.V. 1993: Topology optimal design and optimal shape design using homogenization. In: Bendsøe, M.P.; Mota Soares, D.A. (eds.);Topology design of structures, pp. 207–218. Dordrecht/Boston: Kluwer

    Google Scholar 

  • Arora, J.S.; Cardoso, J.B. 1992: Variational principle for shape design sensitivity analysis.AIAA J. 30, 538–547

    Google Scholar 

  • Arora, J.S.; Lin, T.C.; Elwakeil, O.; Huang, M.W. 1995:IDESION User's manual version 4.2. Optimal Design Laboratory, College of Engineering, The University of Iowa, Iowa City.

    Google Scholar 

  • Bendsøe, M.P.; Kikuchi, N. 1988: Generating optimal topology in structural design using a homogenization method.Comp. Meth. Appl. Mech. Eng. 71, 197–224

    Google Scholar 

  • Bendsøe, M.P.; Guedes, J.M.; Haber, R.B.; Pedersen P; Taylor, J.E. 1994: An analytical model to predict optimal material properties in the context of optimal structural design.ASME J. Appl. Mech. 61, 930–937

    Google Scholar 

  • Bendsøe, M.P.; Diaz, A.R.; Lipton, R.; Taylor, J.E. 1995: Optimal design of material properties and material distribution for multiple loading conditions.Int. J. Num. Meth. Eng. 38, 1149–1170

    Google Scholar 

  • Chen, T.M. 1993:Micromechanics and effective properties of particulate composites and fluid suspensions. Ph.D. Dissertation, Department of Civil Engineering and Operations Research, Princeton University

  • Dasgupta, A.; Agarwal, R.K. 1992: Orthotropic thermal conductivity of plain-weave fabric composites using a homogenization technique.J. Comp. Mat. 26, 2736–2758

    Google Scholar 

  • Diaz, A.; Sigmund, O. 1995: Checkerboard patterns in layout optimization.Struct. Optim. 10, 40–45

    Google Scholar 

  • Eshelby, J. 1957: The determination of the elastic field of an ellipsoidal inclusion and related problems.Proc. Roy. Soc., London A241, 379–396

    Google Scholar 

  • Grabovsky, Y.; Kohn, R.V. 1994: Microstructures minimizing the energy of a two phase elastic composite in two space dimensions. 1: The confocal ellipse construction.J. Mech. Phys. Solids 43, 933–947

    Google Scholar 

  • Grabovsky, Y.; Kohn, R.V. 1995: Microstructures minimizing the energy of a two phase elastic composite in two space dimensions. 2: The confocal Vigdergauz microstructure.J. Mech. Phys. Solids 43, 949–969

    Google Scholar 

  • Guedes, J.; Kikuchi, N. 1991: Preprocessing and postprocessing for materials based on the homogenization method and adaptive finite element methods.Comp. Meth. Appl. Mech. Eng. 83, 143–198

    Google Scholar 

  • Haber, R.B.; Jog, C.S.; Bendsøe, M.P. 1996: A new approach to variable-topology design using a constraint on perimeter.Struct. Optim. 11, 1–12

    Google Scholar 

  • Hashin, Z. 1962: The elastic moduli of heterogeneous materials,ASME J. Appl. Mech. 29, 143–150

    Google Scholar 

  • Hinton, E.; Sienz, J. 1994: Aspects of adaptive finite element analysis and structural optimization. In: Topping, B.H.V.; Papadrakakis, M. (eds.)Advances in structural optimization, pp. 1–25. Edinburgh: Civil-Comp Press

    Google Scholar 

  • Huang, M.W.; Arora, J.S. 1996: A self-scaling implicit SQP method for large scale structural optimization.Int. J. Num. Meth. Eng. 39, 3305–3325

    Google Scholar 

  • Jog, C.S.; Haber, R.B.; Bendsøe, M.P. 1994: Topology design with optimized, self-adaptive materials.Int. J. Num. Meth. Eng. 37, 1323–1350

    Google Scholar 

  • Jog, C.S.; Haber, R.B. 1996: Stability of finite element models for distributed-parameter optimization and topology design.Comp. Meth. Appl. Mech. Eng. 130, 203–226

    Google Scholar 

  • Johanson, R.; Kikuchi, N.; Papalambros, P. 1994: Simultaneous topology and material microstructure design. In: Topping, B.H.V.; Papadrakakis, M. (eds.)Advances in structural optimization, pp. 143–150. Edinburgh: Civil-Comp Press

    Google Scholar 

  • Kohn, R.V.; Strang, G. 1986: Optimal design and relaxation and relaxation of variational problems.Comm. Appl. Math. 39, 1–25 (Part I), 139–182 (Part II), 353–377 (Part III)

    Google Scholar 

  • Lakes, R.S. 1987: Foam structures with a negative Poisson's ratio.Science 235, 1038–1040

    Google Scholar 

  • Lakes, R.S. 1991: Experimental micro mechanics methods for conventional and negative Poisson's ratio cellular solids as Cosserat continua.J. Eng. Mat. Tech. 113, 148–155

    Google Scholar 

  • Lakes, R.S. 1993: Materials with structural hierarchy.Nature 361, 511–515

    Google Scholar 

  • Lurie, K.A.; Cherkaev, A.V. 1986: Effective characteristics of composite materials and optimal design of structural elements.Int. J. Adv. Mech. 9, ???-???. (Translated from Russian by Natalie Alexeev)

    Google Scholar 

  • Milton, G.W. 1990: On characterizing the set of possible effective tensors of composites: the variational method and the translational method.Comm. Appl. Math. 43, 63–125

    Google Scholar 

  • Milton, G.W. 1992: Composite materials with Poisson's ratios close to-1.J. Mech. Phys. Solids 40, 1105–1137

    Google Scholar 

  • Muskhelishvili, N.I. 1953:Some basic problems of the mathematical theory of elasticity. Groningen: P. Noordhoof Ltd.

    Google Scholar 

  • Olhoff, N.; Bendsøe, M.P.; Rasmussen, J. 1991: On CAD-integrated structural topology and design optimization.Comp. Meth. Appl. Mech. Eng. 89, 259–279

    Google Scholar 

  • Pedersen, P. 1990: Bounds on elastic energy in solids of orthotropic materials.Struct. Optim. 2, 55–63

    Google Scholar 

  • Ramm, E.; Bletzinger, K.-U.; Reitinger, R.; Maute, K. 1994: The challenge of structural optimization. In: Topping, B.H.V.; Papadrakakis, M. (eds.)Advances in structural optimization, pp. 27–53. Edinburgh: Civil-Comp Press

    Google Scholar 

  • Reuss, A. 1929: Berücksichtigung der elastischen Formänderung in der Plastizitättheorie,Z. Angew. Math. Mech. 9, 266–274

    Google Scholar 

  • Rodrigues, H.; Fernandes, P. 1995: A material based model for topology optimization of thermoelastic structures.Int. J. Num. Meth. Eng. 38, 1151–1965

    Google Scholar 

  • Rozvany, G.I.N. 1989:Structural design via optimality criteria. Dordrecht: Kluwer

    Google Scholar 

  • Schittkowski, K. 1985: A unified outline of nonlinear programming algorithms.J. Mech., Trans. Auto. Des. 107, 399–453

    Google Scholar 

  • Sigmund, O. 1994: Design of material structures using topology optimization.Report S69. Danish Center for Applied Mathematics and Mechanics.

  • Suquet, P.M. 1985: Approach by homogenization of some linear and nonlinear problems in solid mechanics. In: Boehler, J.P. (ed.)Plastic behavior of anisotropic solids. Proc. CNRS Int. Colloq. 319

  • Suquet, P.M. 1985: Local and global aspects in the mathematical theory of plasticity. In: Sawczuk A.; Bianchi, G. (eds.)Plasticity today: modelling methods and applications, pp. 279–310. London: Elsevier

    Google Scholar 

  • Suquet, P.M. 1987: Elements of homogenization for inelastic solid mechanics. In: Sanchez-Palencia, E.; Zaoui, A. (eds.)Homogenization techniques for composite media, pp. 193–278, Berlin, Heidelberg, New York: Springer

    Google Scholar 

  • Swan, C.C. 1994: Techniques for stress and strain controlled homogenization of inelastic periodic composites.Comp. Meth. Appl. Mech. Eng. 117, 249–267

    Google Scholar 

  • Swan, C.C.; Kosaka, I. 1996a: Homogenization-based analysis and design of composites,Comp. & Struct. (in press)

  • Swan, C.C.; Kosaka, I. 1996b: Voigt-Reuss topology optimization for structures with linear elastic material behaviors.Int. J. Num. Meth. Eng. (accepted)

  • Swan, C.C.; Kosaka, I. 1996c: Voigt-Reuss topology optimization for structures with nonlinear material behaviors.Int. J. Num. Meth. Eng. (submitted)

  • Swan, C.C.; Arora, J.S.; Kosaka I.; Huang, M.W. 1996: Structural topology design solutions using SLP and classical mixing rules. (Submitted)

  • Thomsen, N.B.; Wang, J.; Karihaloo, B.L. 1994: Optimization — a tool in advanced materials technology,Struct. Optim. 8, 9–15

    Google Scholar 

  • Todoroki, A.; Watanabe, K.; Kobayashi, H.; Nakamura, H. 1995: Optimization of composite plate by genetic algorithms.Trans. Japan Soc. Mech. Engrs., Part A 61–587, 1453–1459

    Google Scholar 

  • Tseng, C.H.; Arora, J.S. 1988: On implementation of computational algorithms for optimal design.Int. J. Num. Meth. Eng. 26, 1365–1402

    Google Scholar 

  • Voigt, W. 1889:Wied Ann. 38

  • Yi, Y.; Luo, S-Y 1992: Modeling of plain weave fabric composite under finite deformation.ASME PVP 248,NE 10, 41–48

    Google Scholar 

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Swan, C.C., Arora, J.S. Topology design of material layout in structured composites of high stiffness and strength. Structural Optimization 13, 45–59 (1997). https://doi.org/10.1007/BF01198375

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