摩擦なし接触を伴う構造物のトポロジー最適化

抄録

Stiffness maximization of structures subjected to frictionless contact is one of fundamental problems in structural optimization. This paper presents a formulation that can be handled with a standard nonlinear programming approach. The frictionless contact problem of an elastic body is formulated as a complementarity problem. Therefore, it is natural to formulate a design optimization problem of structures subject to frictionless contact as a mathematical programming problem with complementarity constraints (MPCC problem). However, since any feasible solution of an MPCC problem does not satisfy standard constraint qualification, conventional nonlinear programming approaches cannot be applied to an MPCC problem. In contrast, the formulation presented in this paper does not involve complementarity constraints, and hence can be solved with a standard nonlinear programming approach. Derivation of this formulation is based on the Lagrange duality applied to an optimization problem defining the compliance.