Peridynamic Formulation for Higher-Order Plate Theory

Abstract

In this study, a new peridynamic model is presented for higher-order plate theory. The formulation is derived by using Euler-Lagrange equation and Taylor’s expansion. The formulation is verified by considering two benchmark problems including simply supported and clamped plates subjected to transverse loading. Moreover, mixed (simply supported-clamped) boundary conditions are also considered to investigate the capability of the current formulation for mixed boundary conditions. Peridynamic results are compared with finite element analysis results and a very good agreement was obtained between the two approaches.

Double horizon peridynamics

“…Here, the material point x = À j lies in the fictitious region, and equation (20) ensures that the fixed Boundary Condition (BC) is satisfied for PD EoM.…”

“…Kefal et al [17] demonstrated how to use peridynamics for topology optimisation of cracked structures. There have also been many studies presenting peridynamic formulations for beams and plates to model isotropic materials [18–22], functionally graded materials [23–28], and composite materials [29,30]. Peridynamics has also been extended to model other physical fields.…”

Distal and non-symmetrical crack nucleation in delamination of plates via dimensionally-reduced peridynamics

“…Papers dealing with two-dimensional peridynamic bodies can be divided into two main categories based on the approach: (1) full 3D numerical simulations [31][32][33], and (2) 2D reduced models [34][35][36][37][38][39][40][41][42][43]. While the former approach has been extensively used to treat delamination explicitly [44][45][46], existing reduced formulation only account for crack propagation with the crack tip oriented normal to the plane and thus cannot capture phenomena such as delamination.…”

Comparison of Peridynamics and Lattice Dynamics Wave Dispersion Relationships

“…Peridynamic Timoshenko beam and Kirchhoff plate formulations are provided in Yang et al [23] and [24], respectively. Peridynamic formulations for higher-order beams and plates are given in Yang et al [25] and [26], respectively. Zhu et al [27] studied polycrystalline fracture by using peridynamics.…”