Robust optimization of structures subjected to frictionless unilateral contact with uncertain initial gaps

This short paper studies a robust optimization problem of a structure subjected to frictionless unilateral contacts. We suppose that initial gaps possess non-probabilistic uncertainty, and attempt to maximize the worst-case sti ff ness of the structure. It is often that a structural optimization problem involving contact conditions is formulated as a mathematical programming problem with complementarity constraints (an MPCC problem). Since any feasible solution of an MPCC problem does not satisfy standard constraint qualifications, special treatment is required to solve an MPCC problem. In contrast, the formulation developed in this paper is free from complementarity constraints, and hence can be handled as a standard nonlinear programming problem. It is shown that this formulation is readily derived as a natural extension of the recently proposed optimal design problem formulation that does not consider uncertainty.