Implementation of peridynamic beam and plate formulations in finite element framework

Research output: Contribution to journalArticle

1 Citation (Scopus)

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

Fingerprint

Continuum mechanics
Crack propagation
continuum mechanics
Mindlin plates
formulations
Integrodifferential equations
Crack initiation
meshfree methods
Buckling
Timoshenko beams
classical mechanics
crack initiation
three dimensional models
crack propagation
buckling
Cracks
differential equations
cracks
propagation
approximation

Keywords

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

Cite this

@article{4e92c471f59d40a487d35100e8dea355,
title = "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.",
keywords = "peridynamic theory, classical continuum mechanics, structural idealization, finite element framework",
author = "Zhenghao Yang and Erkan Oterkus and {Tien Nguyen}, Cong and Selda Oterkus",
year = "2018",
month = "6",
day = "11",
doi = "10.1007/s00161-018-0684-0",
language = "English",
journal = "Continuum Mechanics and Thermodynamics",
issn = "0935-1175",

}

TY - JOUR

T1 - Implementation of peridynamic beam and plate formulations in finite element framework

AU - Yang, Zhenghao

AU - Oterkus, Erkan

AU - Tien Nguyen, Cong

AU - Oterkus, Selda

PY - 2018/6/11

Y1 - 2018/6/11

N2 - 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.

AB - 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.

KW - peridynamic theory

KW - classical continuum mechanics

KW - structural idealization

KW - finite element framework

UR - https://link.springer.com/journal/161

U2 - 10.1007/s00161-018-0684-0

DO - 10.1007/s00161-018-0684-0

M3 - Article

JO - Continuum Mechanics and Thermodynamics

T2 - Continuum Mechanics and Thermodynamics

JF - Continuum Mechanics and Thermodynamics

SN - 0935-1175

ER -