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

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We present a nonintrusive 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 uncertainties 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 projection scheme. We then develop a nonintrusive quadrature-based formulation to evaluate the robustness metric and the associated shape derivative. The formulation is nonintrusive in the sense that it works with any level-set-based topology optimization code that can provide deterministic displacements, outputs, and shape derivatives for selected stochastic parameter values. We demonstrate the effectiveness of the proposed approach on various problems under loading and material uncertainties.