Equilibrium problem for elastic plate with thin rigid inclusion crossing an external boundary

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Abstract

The paper concerns an equilibrium problem for an elastic plate with a thin rigid inclusion. Both vertical and horizontal displacements of the plate are considered in the frame of the model. It is assumed that the inclusion crosses the external boundary of the plate. Moreover, the inclusion is delaminated from the plate which leads to appearance of a crack between the inclusion and the plate. To provide a mutual nonpenetration between crack faces, we consider nonlinear boundary conditions with unknown set of a contact. We prove a solution existence of the equilibrium problem and analyze an inverse problem with unknown elasticity tensor. To formulate the inverse problem, additional data are imposed to be determined from a boundary measurement. An existence of a solution to the inverse problem is proved, and stability properties are established.

Original languageEnglish
Article number121
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume72
Issue number3
DOIs
Publication statusPublished - Jun 2021

Keywords

  • Crack
  • Elastic plate
  • Free boundary problem
  • Inverse problem
  • Thin rigid inclusion
  • Variational inequality

OECD FOS+WOS

  • 1.01 MATHEMATICS
  • 1.03 PHYSICAL SCIENCES AND ASTRONOMY

State classification of scientific and technological information

  • 27 MATHEMATICS

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