Design optimization in unilateral contact using pressure constraints and Bayesian optimization

TL;DR

This paper compares gradient-based and Bayesian optimization methods for shape design in unilateral contact problems, demonstrating their effectiveness and limitations through numerical examples involving pressure constraints.

Contribution

It introduces a combined approach using both gradient-based and Bayesian optimization for contact design problems with pressure constraints, highlighting their comparative performance.

Findings

Both methods perform reasonably well on nonsmooth contact problems.

Bayesian optimization effectively handles pressure constraints without gradient information.

Gradient-based methods provide accurate sensitivities for optimization.

Abstract

Design optimization problems, e.g., shape optimization, that involve deformable bodies in unilateral contact are challenging as they require robust contact solvers, complex optimization methods that are typically gradient-based, and sensitivity derivations. Notably, the problems are nonsmooth, adding significant difficulty to the optimization process. We study design optimization problems in frictionless unilateral contact subject to pressure constraints, using both gradient-based and gradient-free optimization methods, namely Bayesian optimization. The contact simulation problem is solved via the mortar contact and finite element methods. For the gradient-based method, we use the direct differentiation method to compute the sensitivities of the cost and constraint function with respect to the design variables. Then, we use Ipopt to solve the optimization problems. For the gradient-free approach, we use a constrained Bayesian optimization algorithm based on the standard Gaussian Process surrogate model. We present numerical examples that control the contact pressure, inspired by real-life engineering applications, to demonstrate the effectiveness, strengths and shortcomings of both methods. Our results suggest that both optimization methods perform reasonably well for these nonsmooth problems.