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.
Reviewer: M.C.Dökmeci


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


Zbl 0628.73122