Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Junction problem for Euler-Bernoulli and Timoshenko elastic inclusions in elastic bodies

Authors: A. M. Khludnev and T. S. Popova
Journal: Quart. Appl. Math. 74 (2016), 705-718
MSC (2010): Primary 35Q74, 49J40
DOI: https://doi.org/10.1090/qam/1447
Published electronically: July 20, 2016
MathSciNet review: 3539029
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Abstract: In the paper, we consider an equilibrium problem for a 2D elastic body with thin Euler-Bernoulli and Timoshenko elastic inclusions. It is assumed that inclusions have a joint point, and we analyze a junction problem for these inclusions. Existence of solutions is proved, and different equivalent formulations of the problem are discussed. In particular, junction conditions at the joint point are found. A delamination of the elastic inclusion is also assumed. In this case, inequality type boundary conditions are imposed at the crack faces to prevent a mutual penetration between crack faces. We investigate a convergence to infinity and to zero of a rigidity parameter of the elastic inclusions. Limit problems are analyzed.

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A. M. Khludnev
Affiliation: Lavrentyev Institute of Hydrodynamics of the Russian Academy of Sciences, and Novosibirsk State University, Novosibirsk 630090, Russia
Email: khlud@hydro.nsc.ru

T. S. Popova
Affiliation: North-Eastern Federal University, Yakutsk, 677000, Russia
Email: ptsokt@mail.ru

DOI: https://doi.org/10.1090/qam/1447
Keywords: Thin inclusion, rigid inclusion, non-penetration condition, crack, variational inequality, junction conditions
Received by editor(s): January 20, 2015
Published electronically: July 20, 2016
Article copyright: © Copyright 2016 Brown University

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