An optimal control problem in polyconvex hyperelasticity
Please always quote using this URN:urn:nbn:de:0296-matheon-11108
- We consider a shape implant design problem that arises in the context of facial surgery. We introduce a reformulation as an optimal control problem, where the control acts as a boundary force. The state is modelled as a minimizer of a polyconvex hyperelastic energy functional. We show existence of optimal solutions and derive - on a formal level - first order optimality conditions. Finally, preliminary numerical results are presented.
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| Author: | Anton Schiela, Lars Lubkoll, Martin Weiser |
|---|---|
| URN: | urn:nbn:de:0296-matheon-11108 |
| Referee: | Peter Deuflhard |
| Document Type: | Preprint, Research Center Matheon |
| Language: | English |
| Date of first Publication: | 2012/03/06 |
| Release Date: | 2012/03/06 |
| Tag: | implant design; optimal control; polyconvex elasticity |
| Institute: | Technische Universität Berlin |
| Zuse Institute Berlin (ZIB) | |
| MSC-Classification: | 49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Jxx Existence theories / 49J20 Optimal control problems involving partial differential equations |
| 65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods | |
| 74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Bxx Elastic materials / 74B20 Nonlinear elasticity | |
| Preprint Number: | 943 |
