New Developments in Handling Stress Constraints in Optimal Material Distributions

There is a general interest to consider stress constraints in topology optimization of continuum structures. By their very nature stress constraints are local constraints which result in large scale optimization problems that are often expensive to solve. Here in order to reduce the computing the effort we explore an alternative technique based on equivalent global (that is integrated) constraints. We define two global stress constraints based on the p-norm and p-mean of the
epsilon-relaxed overall stress criteria in the finite elements. We present a new formulation of the epsilon-relaxation technique which is better suited to topology optimization of continuum structures and which makes the relaxation process automatic. The "p-mean" and "p-norm"
functions bound by lower and upper value the maximum value of the epsilon-relaxed overall stress criterion. Based on numerical experiments this study compares the global and the local constraint formulations. Even if the use of integrated constraints leads a reduction
of the computing time by one or two orders of magnitude, they definitely give a weaker control of local stress level. This sometimes can lead to solutions that are a bit different.