Geodesic
A certain approach to solving of some one-dimensional contact problems
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 1, pp. 77-84

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The paper deals with the problems of the unbonded contact of beams, strings, circular membranes and plates. A new approach to solving of such problems is suggested. This approach includes the rigorous problem statement, the elementary proof of the uniqueness of solution and the analytical solution construction method. The method is based on the iterative correction of the contact region. A number of examples of this method application are given. 
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M. A. Osipenko; Yu. I. Nyashin. A certain approach to solving of some one-dimensional contact problems. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 1, pp. 77-84. http://geodesic.mathdoc.fr/item/ISU_2011_11_1_a9/