Topology optimization of contact problems using Cahn- Hilliard regularization

Abstract eng:
The paper is concerned with the topology optimization of elastic bodies in unilateral contact with a given friction. The aim of the optimization problem is to find such distribution of the material density function to minimize the normal contact stress. The phase field approach is used to analyze and solve numerically this optimization problem. The original cost functional is regularized using GinzburgLandau free energy functional including the surface and bulk energy terms. These terms allow to control global perimeter constraint and the occurrence of the intermediate solution values. The Lagrangian approach is used to calculate the derivative of the regularized cost functional and to formulate a necessary optimality condition. The optimal topology is obtained as the steady state of the phase transition governed by modified Cahn-Hilliard equation. The finite difference and finite element methods are used as the discretization methods. Numerical examples are provided and discussed.

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