Haslinger, J.; Neittaanmäki, P. On the existence of optimal shapes in contact problems. (English) Zbl 0559.73099 Numer. Funct. Anal. Optimization 7, 107-124 (1984). 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. Cited in 10 Documents 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 Keywords:minimization of total energy of system in equilibrium state; optimal shape design; two-dimensional elastic body; rigid frictionless foundation; boundary part; unilateral boundary conditions; solvability PDF BibTeX XML Cite \textit{J. Haslinger} and \textit{P. Neittaanmäki}, Numer. Funct. Anal. Optim. 7, 107--124 (1984; Zbl 0559.73099) Full Text: DOI 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) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.