Exploiting Lagrange duality for topology optimization with frictionless unilateral contact

TL;DR

This paper introduces a new approach for topology optimization of structures with frictionless unilateral contact, using Lagrange duality to avoid complementarity constraints and enable standard optimization methods.

Contribution

It develops tractable reformulations for contact problems in topology optimization based on Lagrange duality, simplifying numerical solution compared to traditional MPCC methods.

Findings

Reformulations avoid complementarity constraints

Numerical experiments demonstrate efficiency

Applicable to trusses and continua

Abstract

This paper presents tractable reformulations of topology optimization problems of structures subject to frictionless unilateral contact conditions. Specifically, we consider stiffness maximization problems of trusses and continua. Based on the Lagrange duality theory, we derive formulations that do not involve complementarity constraints. It is often that a structural optimization problem with contact conditions is formulated as a mathematical programming problem with complementarity constraints (MPCC problem). However, MPCC usually requires special treatment for numerical solution, because it does not satisfy standard constraint qualifications. In contrast, to the formulation presented in this paper, we can apply standard optimization approaches. Numerical experiments of trusses and continua are performed to examine efficiency of the proposed approach.