Robust topology optimization of static systems with unilateral frictional contact

Abstract

In this paper a robust topology optimization algorithm for linear elastic structures in unilateral contact is presented. The deformation of the linear elastic structure is constrained by support structures that are modeled with the help of Signorini’s contact conditions. The contact conditions in turn are enforced with the augmented Lagrangian approach. Doing so, the robust optimization considers uncertainties at the support such as manufacturing tolerances and its local friction behavior. Due to high numerical costs in robust optimization, the first-order second-moment approach is used to approximate the mean and variance of the objective. This approximation results in minimal additional costs to approximate the mean, the variance and their gradients. Consequentially, a gradient-based optimization algorithm can be used to minimize a weighted sum of both. The results show that the presented approach indeed improves the robustness with respect to uncertain contact conditions compared to a deterministic optimization.