Optimal control of a two-dimensional contact problem

Abstract

We consider a frictionless contact problem with unilateral constraints for a 2D bar. We describe the problem, then we derive its weak formulation, which is in the form of an elliptic variational inequality of the first kind. Next, we establish the existence of a unique weak solution to the problem and prove its continuous dependence with respect to the applied tractions and constraints. We proceed with the study of an associated control problem for which we prove the existence of an optimal pair. Finally, we consider a perturbed optimal control problem for which we prove a convergence result.

Keywords:

• Contact problem
• unilateral constraint
• variational inequality
• weak solution
• optimal control
• convergence results

AMS Subject Classifications:

• 74M15
• 49J40
• 49J45
• 49J20

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Université de Perpignan Via Domitia (UPVD) .