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**Shape optimization in contact problems with friction.**
*(English)*
Zbl 0628.73123

The paper is concerned with the optimal shape design of a two-dimensional elastic body in contact with a rigid foundation. The influence of the friction between the body and its foundation is taken into account by applying the simple model with a given friction. The contact boundary of the elastic body with unilateral boundary conditions is redesigned in such a way that the total potential energy of the system in the equilibrium state is minimized. First, the solvability of this contour design problem is examined, and the existence of a solution is proved. Then, a finite element discretization with linear triangular elements as well as the sensitivity analysis is presented. This is a theoretical analysis on the shape optimization of elastic structures in contact problems.

The paper with no application is a continuation of the authors’ work on the subject [see the citations in the article reviewed above (Zbl 0628.73122)]; it should appeal to investigators in the area of structure optimization.

The paper with no application is a continuation of the authors’ work on the subject [see the citations in the article reviewed above (Zbl 0628.73122)]; it should appeal to investigators in the area of structure optimization.

Reviewer: M.C.Dökmeci

### MSC:

74A55 | Theories of friction (tribology) |

74M15 | Contact in solid mechanics |

74P99 | Optimization problems in solid mechanics |

74S05 | Finite element methods applied to problems in solid mechanics |