Implementation of peridynamic beam and plate formulations in finite element framework

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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.
Original languageEnglish
Number of pages15
JournalContinuum Mechanics and Thermodynamics
Early online date11 Jun 2018
DOIs
Publication statusE-pub ahead of print - 11 Jun 2018

Keywords

  • peridynamic theory
  • classical continuum mechanics
  • structural idealization
  • finite element framework

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