Optimal Control Problems in Finite-Strain Elasticity by Inner Pressure and Fiber Tension

• Main Authors: Günnel, Andreas, Herzog, Roland
• Other Authors: Frontiers Research Foundation,
• Format: Article
• Language: English
• Published: Universitätsbibliothek Chemnitz 2016
• Subjects: Optimalsteuerung; Elastizität; quasi-Newton-Verfahren; Mehrgitter-Vorkonditionierung; Optimierung; Finite-Elemente-Methode; Technische Universität Chemnitz; Publikationsfonds; optimal control; finite-strain elasticity; quasi-Newton method; multigrid preconditioning; optimization; finite element method; Publication fund; ddc:518
• Online Access: http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-209295; http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-209295; http://www.qucosa.de/fileadmin/data/qucosa/documents/20929/fams-02-00004.pdf; http://www.qucosa.de/fileadmin/data/qucosa/documents/20929/signatur.txt.asc

Optimal control problems for finite-strain elasticity are considered. An inner pressure or an inner fiber tension is acting as a driving force. Such internal forces are typical, for instance, for the motion of heliotropic plants, and for muscle tissue. Non-standard objective functions relevant for elasticity problems are introduced. Optimality conditions are derived on a formal basis, and a limited-memory quasi-Newton algorithm for their solution is formulated in function space. Numerical experiments confirm the expected mesh-independent performance.