Level set shape and topology optimization of finite strain bilateral contact problems

TL;DR

This paper introduces a comprehensive level set-based optimization method for multi-material structures under finite strain conditions, effectively handling large deformations, contact, and separation to improve design performance.

Contribution

It develops a novel framework combining explicit level set geometry, finite element discretization, and nonlinear programming for shape and topology optimization under finite strains.

Findings

Enhanced design performance over small strain models

Ability to handle large motion sliding contact and separation

Generation of non-intuitive, load path-dependent designs

Abstract

This paper presents a method for the optimization of multi-component structures comprised of two and three materials considering large motion sliding contact and separation along interfaces. The structural geometry is defined by an explicit level set method, which allows for both shape and topology changes. The mechanical model assumes finite strains, a nonlinear elastic material behavior, and a quasi-static response. Identification of overlapping surface position is handled by a coupled parametric representation of contact surfaces. A stabilized Lagrange method and an active set strategy are used to model frictionless contact and separation. The mechanical model is discretized by the extended finite element method which maintains a clear definition of geometry. Face-oriented ghost penalization and dynamic relaxation are implemented to improve the stability of the physical response prediction. A nonlinear programming scheme is used to solve the optimization problem, which is regularized by introducing a perimeter penalty into the objective function. Sensitivities are determined by the adjoint method. The main characteristics of the proposed method are studied by numerical examples in two dimensions. The numerical results demonstrate improved design performance when compared to models optimized with a small strain assumption. Additionally, examples with load path dependent objectives display non-intuitive designs.