ISBN 978-3-8439-4963-7

978-3-8439-4963-7, Reihe Mathematik

Anna Walter
Optimal Control of Nonlinear Elastoplasticity Problems with Model Order Reduction

163 Seiten, Dissertation Technische Universität Darmstadt (2021), Softcover, B5

Zusammenfassung / Abstract

The topic of this work is the optimal control of deep drawing processes based on reduced models. The aim is to optimize the deep drawing process with respect to the blankholder force and the internal fluid pressure in order to ensure a failure-free production.

The deep drawing process can be modeled as an elastoplastic problem with frictional contact. Large deformations occur, thus we have to deal with a multiplicative decomposition of the deformation gradient. This leads to a highly nonlinear system. Moreover, we have to deal with complementarity systems, which are non-smooth and thus do not allow the application of the classical Newton method. Therefore, the principle of semismoothness is used in order to be able to apply a semismooth variant of Newton's method. The solving time of the Newton method is dominated by two main aspects. A sufficiently accurate discretization of the domain leads to a high-dimensional system of equations. Solving this system over all Newton iterations thereby accounts for a large part of the computation time. Therefore, the dimension of the state space is reduced, resulting in a lower dimensional system of equations and a significant reduction in runtime. Another aspect is the evaluation of the nonlinear functions. To make this more efficient, the basic idea is to evaluate the nonlinear functions only at specific points and interpolate the remaining values. These two reduction techniques are used to solve the optimal control problem efficiently in MATLAB to determine the optimal control of a simplified deep drawing process.