We consider the nonlinear equilibrium problem for a plate subject to the Signorini condition on a part of the boundary. We construct a family of auxiliary problems in extended domains such that solutions of the auxiliaries problems converge to a solution of the Signorini problem. Each problem of this family describes the equilibrium state of a plate containing a crack. A boundary nonpenetration condition in the form of an inequality is imposed on the crack. We also discuss the equivalent differential statement of the problem. Bibliography: 11 titles. Illustrations: 3 figures.
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Translated from Vestnik Novosibirskogo Gosudarstvennogo Universiteta: Seriya Matematika, Mekhanika, Informatika 13, No. 1, 2013, pp. 91–104.
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Lazarev, N.P. Fictitious Domain Method in the Equilibrium Problem for a Timoshenko Type Plate Contacting with a Rigid Obstacle. J Math Sci 203, 527–539 (2014). https://doi.org/10.1007/s10958-014-2156-9
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DOI: https://doi.org/10.1007/s10958-014-2156-9