*URN to cite this document:*urn:nbn:de:bvb:703-epub-4465-4

## Title data

Schiela, Anton ; Stöcklein, Matthias:

**Algorithms for Optimal Control of Elastic Contact Problems with Finite Strain.**

University Bayreuth
,
2019
. - 21 S.

PDF
publication.pdf - Preprint Available under License Creative Commons BY 4.0: Attribution . Download (3MB) |

## Project information

Project financing: |
Deutsche Forschungsgemeinschaft DFG grant SCHI 1379/2-1 within the priority programme SPP 1962 |
---|

## Abstract

Optimal control of hyperelastic contact problems in the regime of finite strains combines various severe theoretical and algorithmic difficulties. Apart from being large scale, the main source of difficulties is the high nonlinearity and non-convexity of the elastic energy functional which precludes uniqueness of solutions and simple local sensitivity results. In addition, the contact conditions add non-smoothness to the overall problem. In this paper, we discuss algorithmic approaches to address these issues. In particular, the non-smoothness is tackled by a path-following approach, whose theoretical properties are reviewed. The subproblems are highly nonlinear optimal control problems, which can be solved by an affine invariant composite step method. For increased robustness and efficiency this method has to be adapted to the particular problem, taking into account its large scale nature, its function space structure and its non-convexity.