Exploiting Lagrange duality for topology optimization with frictionless unilateral contact

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.