Variational approach to modeling soft and stiff interfaces in the Kirchhoff-Love theory of plates

Alexey Furtsev, Evgeny Rudoy

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

Within the framework of the Kirchhoff-Love theory, a thin homogeneous layer (called adhesive) of small width between two plates (called adherents) is considered. It is assumed that elastic properties of the adhesive layer depend on its width which is a small parameter of the problem. Our goal is to perform an asymptotic analysis as the parameter goes to zero. It is shown that depending on the softness or stiffness of the adhesive, there are seven distinct types of interface conditions. In all cases, we establish weak convergence of the solutions of the initial problem to the solutions of limiting ones in appropriate Sobolev spaces. The asymptotic analysis is based on variational properties of solutions of corresponding equilibrium problems.

Original languageEnglish
Pages (from-to)562-574
Number of pages13
JournalInternational Journal of Solids and Structures
Volume202
DOIs
Publication statusPublished - 1 Oct 2020

Keywords

  • Asymptotic analysis
  • Biharmonic equation
  • Bonded structure
  • Composite material
  • Interface conditions
  • Kirchhoff-Love plate
  • DERIVATION
  • QUASI-STATIC DELAMINATION
  • ASYMPTOTIC ANALYSIS
  • ELASTIC INCLUSIONS
  • EQUILIBRIUM
  • BOUNDARY
  • NUMERICAL-SIMULATION
  • IMPERFECT INTERFACE

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