Titelaufnahme

GesamttitelOptimal control of perfect plasticity / C. Meyer, S. Walther
Titel
Part I (January 2020) Stress tracking
VerfasserMeyer, Christian ; Walther, Stephan
ErschienenJanuary 2020
Ausgabe
Elektronische Ressource
Umfang1 Online-Ressource (29 Seiten) : Illustrationen
SerieErgebnisberichte angewandte Mathematik ; no. 623
URNurn:nbn:de:hbz:6:2-126025 
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Stress tracking [1 mb]
Zusammenfassung

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 eld is unique. This gives rise to a well de ned control-to-state operator, which is continuous but not Ga^teaux-di erentiable. The control-to-state map is therefore regularized, rst 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.

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