The paper deals with a phase field model for formulation and solution of the topology optimization problems of bodies in unilateral contact consisting in the normal contact stress minimization. The contact problem with Tresca friction is governed by the system of elasticity equations with inequality type boundary conditions. The structural optimization problem consists in finding such material distribution within design domain to minimize the normal contact stress along the boundary of the

more »

... The original structural optimization problem is reformulated in terms of material density function. Moreover the original cost functional is regularized using also surface and bulk energy terms. These terms allow to control global perimeter constraint and the occurence of the intermediate solution values. Using Lagrange multiplier approach the derivative of the regularized cost functional with respect to the control variable is calculated. The neccessary optimality condition is formulated in the form of Allen-Cahn gradient flow equation. The optimal topology is obtained as the steady state of the phase transition governed by this equation. This equation is discretized using finite difference and finite element methods. Numerical examples are provided.