Compliance optimization of a continuum with bimodulus material under multiple load cases

Topology optimization of a continuum with bimodulus material under multiple load cases (MLC) is investigated by using material replacement method. Using traditional methods to solve such a problem will encounter two difficulties for the sake of the stress-dependent behavior of bimodulus material. One is the nonlinear behavior of bimodulus material. The other is the definition of local material property under MLC. The present method can overcome the difficulties easily. It contains three major aspects. Firstly, the bimodulus material is replaced with two isotropic materials in optimization. Secondly, the local stiffness is modified according to the stress states because of material replacement. Meanwhile, which one of the isotropic materials to be adopted for each element in the next structural analysis in optimization is determined by the replacement criterion under MLC, i.e., comparing the local CSED (strain energy density (SED) caused by compression stresses) and the TSED (SED caused by tension stresses), the isotropic material which modulus equal to the compression modulus of bimodulus material is used as the material properties of the element if the CSED is greater than the TSED, or vice versa. Finally, the relative densities of elements as the design variables are updated using a gradient-based method. As the reanalysis with respect to material properties for obtaining the accurate deformation is merged into the global iterations of optimization, the efficiency of optimization is highly improved. Numerical examples are given to express the validity and high efficiency of the present method. Results also show that the difference between tension modulus and compression modulus influences the optimal topology of a structure with bimodulus material under MLC, obviously.