Continuum Mechanics and Thermodynamics

, Volume 31, Issue 1, pp 301–315 | Cite as

Implementation of peridynamic beam and plate formulations in finite element framework

  • Zhenghao Yang
  • Erkan OterkusEmail author
  • Cong Tien Nguyen
  • Selda Oterkus
Open Access
Original Article


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 Beam Plate Fracture Finite element 



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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Zhenghao Yang
    • 1
  • Erkan Oterkus
    • 1
    Email author
  • Cong Tien Nguyen
    • 1
  • Selda Oterkus
    • 1
  1. 1.Department of Naval Architecture, Ocean and Marine EngineeringUniversity of StrathclydeGlasgowUK

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