Topology Optimization of Thermoelastic Structures Using Level Set Method

This paper describes the topology optimization of thermoelastic structures, using level set method. The objective is to minimize the mean compliance of a structure with a single material volume constraint. We first implemented SIMP method for the present compliance minimization problem of thermoelastic struc-tures. We find that large area of “gray ” densities, or the underlying isotropic microstructures, still arise in the optimal structures given by SIMP method. We attempted to get rid of such “gray ” densities by increasing the penalty parameter, but this still does not guarantee “black and white ” designs. The magnitude of penalty which is big enough to generate a “black and white ” design actually depends on boundary and loading conditions, and it is not known a priori. Moreover, big penalty will often leads to local optimal results whose performance is poor. Actually, the structures with “gray ” densities represents the best solution to the SIMP formulation of the present optimization problem. However, with the present fabrication technology, it is still hard or costly to fab-ricate such microstructures. Therefore, in common engineering applications, the optimal structure coming with microstructure is not feasible. In view of the above mentioned issues, we applied level set beased boundary variation method for the opti-mization problem. In level set based method, free boundary of a structure is considered as design variable, and i