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

Haslinger, J.; Horák, V.; Neittaanmäki, P.

Numer. Funct. Anal. Optimization 8(1985-86), 557-587 (1986).

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

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

Keywords:

optimal shape design; two-dimensional elastic body; rigid foundation; friction; unilateral boundary conditions; total potential energy; equilibrium state; minimized; existence; linear triangular elements; sensitivity analysis

Citations:

Zbl 0628.73122