Authors: Meyer, Christian
Walther, Stephan
Title: Optimal control of perfect plasticity Part II: Displacement 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 optimize the displacement field in the domain occupied by the body by means of prescribed Dirichlet boundary data, which serve as control variables. The arising optimization problem is nonsmooth for several reasons, in particular, since the control-to-state mapping is not single-valued. We therefore apply a Yosida regularization to obtain a single-valued control-to-state operator. Beside the existence of optimal solutions, their approximation by means of this regularization approach is the main subject of this work. It turns out that a so-called reverse approximation guaranteeing the existence of a suitable recovery sequence can only be shown under an additional smoothness assumption on at least one optimal solution.
Subject Headings: optimal control of variational inequalities
reverse approximation
Yosida regularization
rate-independent systems
perfect plasticity
Issue Date: 2020-03
Appears in Collections:Ergebnisberichte des Instituts für Angewandte Mathematik

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