Optimization of Structure & Material Properties for Solids Composed of Softening Material
An existing formulation for the prediction of the optimal material properties tensor for systems made of linear material is extended here to encompass design with nonlinear softening material. The original model for the linear case was stated as a convex, constrained nonlinear programming problem, and this property is preserved in the extension. The development is exemplified for the case of design for minimum global compliance. An extremum problem formulation for elastostatics is incorporated into the design problem, as a convenient way to model the structural analysis of general softening systems. Unlike the case for design with linear material, in the nonlinear problem the form of the solution for optimal material properties, and the associated stress fields as well, evolve with increasing load. Computational results are presented for a two-dimensional example problem, in which a system is designed for different loads while parameters in the material model are held fixed.
KeywordsNonlinear Programming Problem Topology Design Material Tensor Linear Material Softening Component
Unable to display preview. Download preview PDF.
- 1.Allaire, G.; Kohn, R.V. (1993b): “Optimal Design for Minimum Weight and Compliance in Plane Stress using Extremal Microstructures.” European J. Mech. A.;1993 (to appear).Google Scholar
- 2.Bendsøe, M.P.; Ben-Tal, A.; Zowe, J. (1993): “Optimization Methods for Truss Geometry and Topology Design.” Structural Optimization (to appear).Google Scholar
- 3.Bendsøe, M.P.; Diaz, A.; Kikuchi, N. (1993): “Topology and Generalized Layout Optimization of Elastic Structures.” loc. cit. Bendsøe and Mota Soares, 1993, pp. 159–206.Google Scholar
- 4.Bendsøe, M.P.; Diaz, A.; Lipton, R.; Taylor, J.E. (1993a): “Optimal Design of Material Properties and Material Distribution for Multiple Loading Conditions.” DCAMM Report no. 469, The Danish Center for Applied Mathematics and Mechanics, The Technical University of Denmark, Lyngby, Denmark, 1993.Google Scholar
- 6.Bendsøe, M.P.; Mota Soares, C.A. (Eds.) (1993): “Topology Optimization of Structures.” Kluwer Academic Press, Dordrecht, The Netherlands, 1993.Google Scholar
- 7.Bendsøe, M.P.; Olhoff, N.; Taylor, J.E. (1993): “A Unified Approach to the Analysis and Design of Elasto-Plastic Structures with Mechanical Contact.” In Rozvany, G.I.N. (Ed.), Optimization of Large Structural Systems, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993, pp. 697–706.Google Scholar
- 8.Jog, C.; Haber, R.B. Bendsøe, M.P. (1993): “Topology Design with Optimized, Self-Adaptive Materials.” Int. J. Num. Meth. Engng. (to appear).Google Scholar
- 9.Milton. G.W., Cherkaev, A.V., “Materials with Elastic Tensors that Range Over the Entire Set Compatible with Thermodynamics,” In Proc. Joint ASCE-ASME-SES MeetW (Herakovich, C.T. & Duva, J.M., Eds.), June 6-9,1993, University of Virginia, Charlottesville, Virginia, USA, p. 342.Google Scholar
- 10.Pedersen, P. (Ed.) (1993): “Optimal Design with Advanced Materials.” Elsevier, Amsterdam, The Netherlands, 1993.Google Scholar
- 13.Sigmund, O. (1993): “Construction of Materials with Prescribed Constitutive Parameters: An Inverse Homogenization Problem.” DCAMM Report no. 470, The Danish Center for Applied Mathematics and Mechanics, The Technical University of Denmark, Lyngby, Denmark, 1993..Google Scholar
- 15.Taylor, J.E. (1993b): “Truss Topology Design for Elastic/Softening Materials.” loc. cit. Bendsøe and Mota Soares, 1993, pp. 451–467.Google Scholar
- 17.Taylor, J.E.; Logo, J. (1993): “Analysis and Design of Elastic/Softening Truss Structures Based on a Mixed-Form Extremum Principle.” In Rozvany, G.I.N. (Ed.), Optimization of Large Structural Systems, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993, pp. 683–696.Google Scholar