- AutorIn
- Dipl.-Math. Andreas Günnel
- Titel
- Numerical Aspects in Optimal Control of Elasticity Models with Large Deformations
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:ch1-qucosa-150930
- Datum der Einreichung
- 04.01.2014
- Datum der Verteidigung
- 19.08.2014
- Abstract (EN)
- This thesis addresses optimal control problems with elasticity for large deformations. A hyperelastic model with a polyconvex energy density is employed to describe the elastic behavior of a body. The two approaches to derive the nonlinear partial differential equation, a balance of forces and an energy minimization, are compared. Besides the conventional volume and boundary loads, two novel internal loads are presented. Furthermore, curvilinear coordinates and a hierarchical plate model can be incorporated into the formulation of the elastic forward problem. The forward problem can be solved with Newton\\\'s method, though a globalization technique should be used to avoid divergence of Newton\\\'s method. The repeated solution of the Newton system is done by a CG or MinRes method with a multigrid V-cycle as a preconditioner. The optimal control problem consists of the displacement (as the state) and a load (as the control). Besides the standard tracking-type objective, alternative objective functionals are presented for problems where a reasonable desired state cannot be provided. Two methods are proposed to solve the optimal control problem: an all-at-once approach by a Lagrange-Newton method and a reduced formulation by a quasi-Newton method with an inverse limited-memory BFGS update. The algorithms for the solution of the forward problem and the optimal control problem are implemented in the finite-element software FEniCS, with the geometrical multigrid extension FMG. Numerical experiments are performed to demonstrate the mesh independence of the algorithms and both optimization methods.
- Freie Schlagwörter (DE)
- Optimalsteuerung, Mehrgitter, Newtonverfahren
- Freie Schlagwörter (EN)
- optimal control, elasticity, multigrid, optimization, newton method
- Klassifikation (DDC)
- 510, 518, 519
- Normschlagwörter (GND)
- Optimale Kontrolle, Elastizität, Optimierung
- GutachterIn
- Prof. Dr. Michael Stingl
- BetreuerIn
- Prof. Dr. Roland Herzog
- Den akademischen Grad verleihende / prüfende Institution
- Technische Universität Chemnitz, Chemnitz
- URN Qucosa
- urn:nbn:de:bsz:ch1-qucosa-150930
- Veröffentlichungsdatum Qucosa
- 22.08.2014
- Dokumenttyp
- Dissertation
- Sprache des Dokumentes
- Englisch