A state-based peridynamic formulation for functionally graded Kirchhoff plates

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Abstract

Functionally graded materials is a potential alternative to traditional fiber reinforced composite materials since they have continuously varying material properties which does not cause stress concentrations. In this study, a state-based peridynamic model is presented for functionally graded Kirchhoff plates. Equations of motion of the new formulation is obtained by using Euler-Lagrange equation and Taylor's expansion. The formulation is verified by considering several benchmark problems including a clamped plate subjected to transverse loading and simply supported plate subjected to transverse loading and inclined loading. The material properties are chosen such that Young's Modulus is assumed to be varied linearly through the thickness direction and Poisson's ratio is constant. Peridynamic results are compared against finite element analysis results and a very good agreement is obtained between the two approaches.
Original languageEnglish
Number of pages22
JournalMathematics and Mechanics of Solids
Early online date13 Oct 2020
DOIs
Publication statusE-pub ahead of print - 13 Oct 2020

Keywords

  • peridynamics
  • Kirchloff plate
  • functionally graded
  • state based
  • Euler-Lagrange equations
  • non-local

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