Authors: Meyer, Christian
Walther, Stephan
Title: Optimal control of perfect plasticity Part I: Stress tracking
Language (ISO): en
Abstract: The paper is concerned with an optimal control problem governed by the rate-independent system of quasi-static perfect elasto-plasticity. The objective is to optimize the stress field by controlling the displacement at prescribed parts of the boundary. The control thus enters the system in the Dirichlet boundary conditions. Therefore, the safe load condition is automatically fulfilled so that the system admits a solution, whose stress field is unique. This gives rise to a well defined control-to-state operator, which is continuous but not Gˆateaux-differentiable. The control-to-state map is therefore regularized, first by means of the Yosida regularization and then by a second smoothing in order to obtain a smooth problem. The approximation of global minimizers of the original non-smooth optimal control problem is shown and optimality conditions for the regularized problem are established. A numerical example illustrates the feasibility of the smoothing approach.
Subject Headings: optimal control of variational inequalities
Dirichlet control problems
first-order necessary optimality conditions
Yosida regularization
rate-independent 15 systems
perfect plasticity
Issue Date: 2020-01
Appears in Collections:Ergebnisberichte des Instituts für Angewandte Mathematik

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