Contact shape optimization: a bilevel programming approach

We consider the problem of shape optimization of nonlinear elastic solids in contact. The equilibrium of the solid is defined by a constrained minimization problem, where the body energy functional is the objective and the constraints impose the nonpenetration condition. Then the optimization problem can be formulated in terms of a bilevel mathematical program. We describe new optimality conditions for bilevel programming and construct an algorithm to solve these conditions based on Herskovits' feasible direction interior point method. With this approach we simultaneously carry out shape optimization and nonlinear contact analysis. That is, the present method is a "one shot" technique. We describe some numerical examples solved in a very efficient way.