Topology Optimization with Different Stress Limit in Tension and Compression

This report presents new progresses in topology optimization of continuum structures with stress constraints. One principal contribution consists in the consideration of equivalent stress criteria which can generalization of von Mises criterion and which are able to take into account non equal stress limits in tension and compression. A literature review led us to consider Raghava and Ishai criteria, which include a contribution of hydrostatic pressure. With the help of these criteria topology optimization can predict more realistic designs in which structural members are able to withstand better tension loads than compression loads, or vice-versa, as it is sometimes encountered in civil engineering or in composite material design. The implementation and sensitivity analysis aspects of Raghava and Ishai criteria in the Finite Element context are presented. We also present recent advanced developments to the solution of topology problems with stress constraints like the stress constraint relaxation technique and the numerical optimization procedure based on convex approximations and dual optimizers. Finally numerical applications will show the original character of the stress based topology designs ad versus compliance designs when there are unequal stress limits or when there are more than one load case.