Topology optimization of continuum structures with local stress constraints

We introduce an extension of current technologies for topology optimization of continuum structures which allows for treating local stress criteria. We rst consider relevant stress criteria for porous composite mate- rials, initially by studying the stress states of the so-called rank 2 layered materials. Then, on the basis of the theoretical study of the rank 2 microstructures, we propose an empirical model that extends the power penalized sti ness model (also called SIMP for Solid Isotropic Microstructure with Penalization for inter- mediate densities). In a second part, solution aspects of topology problems are considered. To deal with the so-called `singularityʹ phenomenon of stress constraints in topology design, an -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.