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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.

MSC:

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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References:

[1] Benedict R.L., 2 pp 1553–
[2] Haslinger J., Ann. Fac. Sci, Tolouse 5 pp 199– (1983) · Zbl 0547.49004
[3] Haslinger J, Math. Meth. Appl. Sci 5 (1984)
[4] Hlavaek I., Numerical solution of variational inequalities (in Slovac) (1982)
[5] Hlaváček I., R.A.I.R.O., Num. Anal 16 pp 351– (1982)
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