On the existence of optimal shapes in contact problems. (English) Zbl 0559.73099

The optimal shape design of a two-dimensional elastic body on a rigid frictionless foundation is analyzed. The problem is to find the boundary part of the body where the unilateral boundary conditions are assumed, in such a way that the total energy of the system in the equilibrium state will be minimized. The solvability of the problem is proved.


74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
74P99 Optimization problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000)
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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