Free Material Optimization: Towards the Stress Constraints

Free material design deals with the question of finding the li ghtest structure subject to one or more given loads when both the distribution of mater i l and the material itself can be freely varied. We additionally consider const raints on local stresses in the optimal structure. We discuss the choice of formulation of the problem and the stress constraints. The chosen formulation leads to a mathe tical program with matrix inequality constraints, so-called nonlinear semidefi nite program. We present an algorithm that can solve these problems. The algorithm is ba sed on a generalized augmented Lagrangian method. A number of numerical examples de monstrates the effect of stress constraints in free material optimization.