Topology Optimization of Continuum Structures with Stress Constraints

We introduce an extension of topology optimization of continuum structures to deal with local stress criteria. We first consider relevant stress criteria for porous composite materials, initially by studying the stress states of the so-called rank 2 layered materials. Then, an empirical model is proposed for the power law materials (also called SIMP materials). In a second part, solution aspects of topology problems are considered. To deal with the so-called 'singularity' phenomenon of stress constraints in topology design, an $\epsilon$ constraint relaxation of the stress constraints is used. We describe the mathematical programming approach that is used to solve the numerical optimization problems. The proposed strategy is applied to illustrative applications.