Peridynamic Higher-Order Beam Formulation

Abstract

In this study, a novel higher-order peridynamic beam formulation is presented. The formulation is obtained by using Euler-Lagrange equations and Taylor’s expansion. To demonstrate the capability of the presented approach, several different beam configurations are considered including simply supported beam subjected to distributed loading, simply supported beam with concentrated load, clamped-clamped beam subjected to distributed loading, cantilever beam subjected to a point load at its free end and cantilever beam subjected to a moment at its free end. Transverse displacement results along the beam obtained from peridynamics and finite element method are compared with each other and very good agreement is obtained between the two approaches.

Double horizon peridynamics

“…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.…”

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.…”

Explicit implementation of the non-local operator method: a non-local dynamic formulation for elasticity solid

“…Various PD models have been proposed over the years, such as bond-based peridynamic (BB-PD) models, state-based peridynamic (SB-PD) models, hybrid models leveraging PD and CCM, and analytical PD solutions. These PD models have been used successfully to tackle a variety of multi-physical issues, such as heat conduction (Bobaru and Duangpanya, 2010;Oterkus et al, 2014), fluid transport (Katiyar et al, 2014;Gao and Oterkus, 2019;Katiyar et al, 2020), material corrosion (Chen and Bobaru, 2015;De Meo et al, 2016;Jafarzadeh et al, 2018), etc., and PD also has been expanded in a variety of directions, such as dual-horizon PD (Ren et al, 2016(Ren et al, , 2017Rabczuk and Zhuang, 2021), PD plate/shell theory (Chowdhury et al, 2016;Zhang et al, 2021;Dorduncu et al, 2021), phase field based PD damage model (Roy et al, 2017(Roy et al, , 2021, wave dispersion analysis in PD (Gu et al, 2016;Butt et al, 2017;Zhang et al, 2019), weak form of PD (Madenci et al, 2018), PD least squares minimisation (Madenci et al, 2019b,a), coupling of FEM and ordinary state-based (OSB)/non-ordinary state-based (NOSB) PD (Yaghoobi and Chorzepa, 2018;Ni et al, 2021;Jin et al, 2021;Liu et al, 2021), higher-order PD (Yang et al, 2021a(Yang et al, , 2021b(Yang et al, , 2021c, etc. In comparison to the local theory, the non-local theory not only has a superior numerical well-posedness, but it also resembles the real physical process better due to its inherent length scale.…”