Topology optimization for minimum stress design with the homogenization method

This paper is devoted to minimum stress design in structural optimization. The homogenization method is extended to such a framework and yields an efficient numerical algorithm for topology optimization. The main idea is to use a partial relaxation of the problem obtained by introducing special microstructures which are sequential laminated composites. Indeed, the so-called corrector terms of such microgeometries are explicitly known, which allows us to compute the relaxed objective function. These correctors can be interpreted as stress amplification factors, caused by the underlying microstructure.