Implementation of peridynamic beam and plate formulations in finite element framework

Abstract

Peridynamic (PD) theory is a new continuum mechanics formulation introduced to overcome the limitations of classical continuum mechanics such as predicting crack initiation and propagation, and capturing nonlocal effects. PD theory is based on integro-differential equations and these equations are generally difficult to be solved by using analytical techniques. Therefore, numerical approximations, especially with meshless method, have been widely used. Numerical solution of three-dimensional models is usually computationally expensive and structural idealization can be utilized to reduce the computational time significantly. In this study, two of such structural idealization types are considered, namely Timoshenko beam and Mindlin plate, and their peridynamic formulations are briefly explained. Moreover, the implementation of these formulations in finite element framework is presented. To demonstrate the capability of the present approach, several case studies are considered including beam and plate bending due to transverse loading, buckling analysis and propagation of an initial crack in a plate under bending loading.

Peridynamics for the thermomechanical behavior of shell structures

“…Recently, Nguyen and Oterkus [19] developed a PD model for 3D beam structures with six degrees of freedom to predict the damages in offshore structures. The bond based PD model for beam and plate developed by Diyaroglu et al [18] is implemented in finite element framework by Yang et al [20]. Chowdhury et al [21] developed a state based peridynamic model for linear elastic shells by introducing curved bond definition.…”

Derivation of dual-horizon state-based peridynamics formulation based on Euler–Lagrange equation

“…PD can also be used for fluid flow simulations [27,28]. Peridynamic formulations for simplified structures, including beams [29,30], plates [31] and shells [32], are also available in the literature. With the advancement of additive manufacturing technologies, fabrication of complex materials such as microstructured materials [33][34][35][36][37][38][39][40][41][42][43][44] is possible.…”

Peridynamic Higher-Order Beam Formulation

“…This formulation was further extended by Yang et al [11] to analyse Kirchhoff plates. O'Grady and Foster [12] developed a non-ordinary state-based model to represent the bending behaviour of Euler-Bernoulli beam. They also introduced a non-ordinary state-based peridynamic model for Kirchhoff-Love plate [13].…”