Robust Level-Set-Based Topology Optimization Under Uncertainties Using Anchored ANOVA Petrov–Galerkin Method

Abstract

. We present a non-intrusive approach to robust structural topology optimization. Specifically, we consider optimization of mean- and variance-based robustness metrics of a linear functional output associated with the linear elasticity equation in the presence of probabilistic un- certainties in the loading and material properties. To provide an efficient approximation of higher-dimensional problems, we approximate the solution to the governing stochastic partial differential equations using the anchored ANOVA Petrov-Galerkin (AAPG) projection scheme. We then develop a non-intrusive quadrature-based formulation to evaluate the robustness metric and the associated shape derivative. The formulation is non-intrusive in the sense that it works with any level-set-based topology optimization code that can provide deterministic displacements, outputs, and shape deriva- tives for selected stochastic parameter values. We demonstrate the effectiveness of the proposed approach on various problems under loading and material uncertainties.