An optimal control problem in polyconvex hyperelasticity
Please always quote using this URN: urn:nbn:de:0297-zib-14745
- 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.
Author: | Lars Lubkoll, Anton Schiela, Martin WeiserORCiD |
---|---|
Document Type: | ZIB-Report |
Tag: | implant design; optimal control; polyconvex elasticity |
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 | |
Date of first Publication: | 2012/02/24 |
Series (Serial Number): | ZIB-Report (12-08) |
ISSN: | 1438-0064 |
ZIB-Reportnumber: | 12-08 |