Exploiting Lagrange duality for topology optimizationwith frictionless unilateral contact

• Published in: Japan journal of industrial and applied mathematics Vol. 37; no. 1; pp. 25 - 48
• Main Author: Kanno, Yoshihiro
• Format: Journal Article
• Language: English
• Published: Tokyo Springer Japan 01.01.2020; Springer Nature B.V
• Subjects: Applications of Mathematics; Computational Mathematics and Numerical Analysis; Mathematical programming; Mathematics; Mathematics and Statistics; Optimization; Original Paper; Stiffness; Topology optimization; Trusses; Unilateral contact; Lagrange duality; 90C25; 90C11; Topology optimization; Nonsmooth mechanics; 49N15; Stiffness maximization; Second-order cone programming
• ISSN: 0916-7005; 1868-937X
• DOI: 10.1007/s13160-019-00375-1

This paper presents tractable reformulations of topology optimization problems of structures subject to frictionless unilateral contact conditions. Specifically, weconsider 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 complementarityconstraints (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 on trusses and continua are performed to examine efficiency of the proposed approach.