Stochastic Topology Design Optimization for Continuous Elastic Materials.

Abstract

In this paper, we develop a stochastic model for topology optimization. We find robust structures that minimize the compliance for a given main load having a stochastic behavior. First, we give some properties about the stability of structures carrying several loads. Then, we propose a stochastic model that takes into account the expected value of the compliance and its variance. We show that, similarly to the case of truss structures, these values can be computed with an equivalent deterministic approach and the stochastic model can be transformed into a nonlinear programming problem, reducing the complexity of this kind of problems. Finally, we check our formulation by considering several 2D and 3D numerical examples. For each benchmark case, we consider a set of optimization problems based on different weight coefficients of the compliance, expected-compliance and variance values and compare the robustness of the obtained solutions between them. We see that considering our methodology with an appropriate set of weight coefficients may help to generate structures robust to main loads and their perturbations.