An Interior Point Algorithm for Optimal Design of Unilateral Constrained Mechanical Systems

We propose a new solving approach for shape optimization (optimal design problem) of elastic solids in contact. As the equilibrium of a solid in contact is a solution of constrained minimization problem for the body energy functional (or an variational inequality), we can consider our optimization problem as a classical bilevel mathematical program (or a generalized bilevel programming problem). We obtain a new optimality conditions for our design problem and construct an algorithm based on Herskovits’ interior point technique to solve it. Numerical examples for hyperelastic plane solids are given.