- Title
- Shape optimization in contact problems with Coulomb friction and a solution-dependent friction coefficient
- Creator
- Beremlijski, Petr; Haslinger, Jaroslav; Outrata, Jiri; Pathó, Róbert
- Date
- 2014
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/76678
- Identifier
- vital:7597
- Identifier
-
https://doi.org/10.1137/130948070
- Identifier
- ISSN:0363-0129
- Abstract
- The present paper deals with shape optimization in discretized two-dimensional (2D) contact problems with Coulomb friction, where the coefficient of friction is assumed to depend on the unknown solution. Discretization of the continuous state problem leads to a system of finite-dimensional implicit variational inequalities, parametrized by the so-called design variable, that determines the shape of the underlying domain. It is shown that if the coefficient of friction is Lipschitz and sufficiently small in the C0,1 -norm, then the discrete state problems are uniquely solvable for all admissible values of the design variable (the admissible set is assumed to be compact), and the state variables are Lipschitzian functions of the design variable. This facilitates the numerical solution of the discretized shape optimization problem by the so-called implicit programming approach. Our main results concern sensitivity analysis, which is based on the well-developed generalized differential calculus of B. Mordukhovich and generalizes some of the results obtained in this context so far. The derived subgradient information is then combined with the bundle trust method to compute several model examples, demonstrating the applicability and efficiency of the presented approach. © 2014 Society for Industrial and Applied Mathematics
- Relation
- SIAM Journal on Control and Optimization Vol. 52, no. 5 (2014), p. 3371-3400
- Rights
- Copyright Society for Industrial and Applied Mathematics Publications
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0102 Applied Mathematics; 0906 Electrical and Electronic Engineering; 0913 Mechanical Engineering; Contact problems; Coulomb friction; Mathematical programs with equilibrium constraints; Shape optimization; Solution-dependent coefficient of friction
- Reviewed
- Hits: 1514
- Visitors: 1485
- Downloads: 0
| Thumbnail | File | Description | Size | Format |
|---|