Optimal Control of Deep Drawing Processes based on Reduced Order Models

Beschreibung

In this thesis we consider a specific class of forming processes, namely deep drawing processes, and in particular the stringer sheet forming process. The goal of this thesis is to state an appropriate optimization model for the optimal control of stringer sheet forming and develop efficient optimization methods. The deep drawing process is a highly nonlinear and nonsmooth process. The physical equilibrium of the deep drawing process is not described by equations and thus no standard optimal control problem. As soon as we deal with elastic bodies in contact, or with nonlinear constitutive laws describing plastic deformations, the equilibrium is described by a more complex model resulting in variational inequalities. The main issue is the handling of the nonlinearities and nonsmoothness which appear in many forms in solid mechanics and possess additional difficulties for the optimization. For the solution of the discretized systems we apply semismooth Newton methods. To reduce the complexity we apply model reduction techniques, which are a very popular tool to reduce the size of complex systems. We apply a nonsmooth optimization which uses subgradient information. For the optimization, the reduced order models are coupled with the proposed Bundle-ROM-based trust region method.

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Daniela Bratzke

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