Fictitious Domain Method in the Equilibrium Problem for a Timoshenko Type Plate Contacting with a Rigid Obstacle

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 thi...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 203; no. 4; pp. 527 - 539
Main Author Lazarev, N. P.
Format Journal Article
LanguageEnglish
Published Boston Springer US 02.12.2014
Springer
Subjects
Mathematics
Mathematics and Statistics
Exterior Boundary
Extended Domain
Equilibrium Problem
Auxiliary Problem
Variational Inequality
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ISSN1072-3374
1573-8795
DOI10.1007/s10958-014-2156-9

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Summary: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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-014-2156-9