Optimization of structure and material properties for solids composed of softening material

Recent results on the design of material properties in the context of global structural optimization provide, in analytical form, a prediction of the optimal material tensor distributions for two or three dimensional continuum structures. The model developed for that purpose is extended here to cover the design of a structure and associated material properties for a system composed of a generic form of nonlinear softening material. As was established in the earlier study on design with linear materials, the formulation for combined ''material and structure'' design with softening materials can be expressed as a convex problem. However, in contrast to the case with linear material, the optimal distribution of material properties predicted in the nonlinear problem depends on the magnitude of load. Computational solutions are presented for several example problems, showing how the optimal designs vary with different values assigned to data that fix the load and material parameters.