New developments in handling stress constraints in optimal material distribution

TLDR

Stress constraints in topology optimization of continuum structures are of great interest but are local, leading to large expensive problems, and are bounded by p‑mean/p‑norm functions of the e‑relaxed overall stress criterion. The study aims to reduce computational effort by developing a new automatic e‑relaxation formulation using equivalent global (integrated) stress constraints for topology optimization of continuum structures. The authors define two global stress constraints derived from the e‑relaxed overall stress criterion, introduce an automatic e‑relaxation formulation using integrated constraints, and compare these global constraints to local formulations through numerical experiments. Integrated constraints reduce computing time by one or two orders of magnitude but provide weaker local stress control, occasionally yielding slightly different solutions.

Abstract

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 effort we explore an alternative technique based on equivalent global (that is integrated) constraints. We define two global stress constraints based on the and of the e-relaxed overall stress criteria in the finite elements. We present a new formulation of the e-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 e-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.