ISBN 9783843903219

978-3-8439-0321-9, Reihe Mathematik

Gerd Wachsmuth
Optimal control of quasistatic plasticity

254 Seiten, Dissertation Technische Universität Chemnitz (2011), Softcover, A5

Zusammenfassung / Abstract

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.