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Multimaterial Topology Optimization of Variational Inequalities

Abstract : The paper is concerned with the analysis and the numerical solution of the multimaterial topology optimization problems for bodies in unilateral contact. The contact phenomenon with Tresca friction is governed by the elliptic variational inequality. The structural optimization problem consists in finding such topology of the domain occupied by the body that the normal contact stress along the boundary of the body is minimized. The original cost functional is regularized using the multiphase volume constrained Ginzburg-Landau energy functional. The first order necessary optimality condition is formulated. The optimal topology is obtained as the steady state of the phase transition governed by the generalized Allen-Cahn equation. The optimization problem is solved numerically using the operator splitting approach combined with the projection gradient method. Numerical examples are provided and discussed.
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Andrzej Myśliński. Multimaterial Topology Optimization of Variational Inequalities. 27th IFIP Conference on System Modeling and Optimization (CSMO), Jun 2015, Sophia Antipolis, France. pp.380-389, ⟨10.1007/978-3-319-55795-3_36⟩. ⟨hal-01626885⟩



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