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978-3-8439-0321-9, Reihe Mathematik
Optimal control of quasistatic plasticity
254 Seiten, Dissertation Technische Universität Chemnitz (2011), Softcover, A5
In this thesis we consider the optimal control problem of quasistatic plasticity with linear kinematic hardening and small strains. This optimal control problem is a mathematical program with complementarity constraints} (MPCC) in function space. We prove necessary optimality conditions of weakly stationary type.
We discuss an implementation of a solution method for the optimal control problem using the FE library FEniCS and present numerical examples which demonstrate the possibility of controlling the springback effect.
In order to give a self-contained presentation, we review the modelling of solid mechanics. Moreover, we recall the definitions and properties of the Bochner-Lebesgue and Bochner-Sobolev spaces and give an introduction to evolution variational inequalities.