Equilibrium of an Elastic Body with Closely Spaced Thin Inclusions

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Abstract

Abstract: Problems with unknown boundaries describing an equilibrium of two-dimensional elastic bodies with two thin closely spaced inclusions are considered. The inclusions are in contact with each other, which means that there is a crack between them. On the crack faces, nonlinear boundary conditions of the inequality type that prevent the interpenetration of the faces are set. The unique solvability of the problems is proved. The passages to the limit as the stiffness parameter of thin inclusions tends to infinity are studied, and limiting models are analyzed.

Original languageEnglish
Pages (from-to)1660-1672
Number of pages13
JournalComputational Mathematics and Mathematical Physics
Volume58
Issue number10
DOIs
Publication statusPublished - 1 Oct 2018

Keywords

  • boundary conditions of mutual nonpenetration
  • crack
  • limiting models
  • stiffness of inclusion
  • thin inclusion
  • CONTACT
  • CRACK
  • ASYMPTOTIC-BEHAVIOR
  • SHAPE SENSITIVITY-ANALYSIS
  • ENERGY INTEGRALS
  • BODIES
  • BOUNDARY
  • NONPENETRATION
  • PLATE
  • RIGID INCLUSION

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