Title: Level set shape and topology optimization of finite strain bilateral contact problems,
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.