1 Department of Mathematics, Technical University of Denmark2 Department of Applied Mathematics and Computer Science, Technical University of Denmark3 Office for Research and Relations, Administration, Technical University of Denmark
We introduce an extension of current technologies for topology optimization of continuum structures which allows for treating 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, and show results for a number of example applications.