Shape optimization design for thermal stress problem in a multiscale structure

Abstract

This study proposes a shape optimization method to minimize the maximum thermal stress of the microstructures in a multiscale structure caused by thermal loading. Using the homogenization method, the homogenized elastic tensors and the homogenized thermal expansion coefficient tensors for the microstructures are calculated to link the microstructures to the macrostructure. The KS function is used to avoid discontinuities and singularities in the maximum thermal stress. Based on the problem formulation, the shape gradient functions are derived for shape optimization.