Topology optimization of cracked structures using peridynamics

Adnan Kefal, Abdolrasoul Sohouli, Erkan Oterkus, Mehmet Yildiz, Afzal Suleman

Research output: Contribution to journalArticle

Abstract

Finite element method (FEM) is commonly used with topology optimization algorithms to determine optimum topology of load bearing structures. However, it may possess various difficulties and limitations for handling the problems with moving boundaries, large deformations, and cracks/damages. To remove limitations of the mesh-based topology optimization, this study presents a robust and accurate approach based on the innovative coupling of Peridynamics (PD) (a meshless method) and topology optimization (TO), abbreviated as PD-TO. The minimization of compliance, i.e., strain energy, is chosen as the objective function subjected to the volume constraint. The design variable is the relative density defined at each particle employing bi-directional evolutionary optimization approach. A filtering scheme is also adopted to avoid the checkerboard issue and maintain the optimization stability. To present the capability, efficiency and accuracy of the PD-TO approach, various challenging optimization problems with and without defects (cracks) are solved under different boundary conditions. The results are extensively compared and validated with those obtained by element free Galerkin method and FEM. The main advantage of the PD-TO methodology is its ability to handle topology optimization problems of cracked structures without requiring complex treatments for mesh connectivity. Hence, it can be an alternative and powerful tool in finding optimal topologies that can circumvent crack propagation and growth in two and three dimensional structures.
LanguageEnglish
Pages1645-1672
Number of pages28
JournalContinuum Mechanics and Thermodynamics
Volume21
Issue number6
Early online date3 Oct 2019
DOIs
Publication statusE-pub ahead of print - 3 Oct 2019

Fingerprint

Shape optimization
topology
optimization
Crack propagation
Bearings (structural)
Topology
Cracks
Finite element method
mesh
Galerkin methods
finite element method
Strain energy
cracks
meshfree methods
Boundary conditions
Galerkin method
crack propagation
Defects
methodology
boundary conditions

Keywords

  • peridynamics
  • topology optimization
  • bi-evolutionary structural optimization
  • cracked structures

Cite this

Kefal, Adnan ; Sohouli, Abdolrasoul ; Oterkus, Erkan ; Yildiz, Mehmet ; Suleman, Afzal. / Topology optimization of cracked structures using peridynamics. In: Continuum Mechanics and Thermodynamics. 2019 ; Vol. 21, No. 6. pp. 1645-1672.
@article{984f456819ae442788515d5d87daa094,
title = "Topology optimization of cracked structures using peridynamics",
abstract = "Finite element method (FEM) is commonly used with topology optimization algorithms to determine optimum topology of load bearing structures. However, it may possess various difficulties and limitations for handling the problems with moving boundaries, large deformations, and cracks/damages. To remove limitations of the mesh-based topology optimization, this study presents a robust and accurate approach based on the innovative coupling of Peridynamics (PD) (a meshless method) and topology optimization (TO), abbreviated as PD-TO. The minimization of compliance, i.e., strain energy, is chosen as the objective function subjected to the volume constraint. The design variable is the relative density defined at each particle employing bi-directional evolutionary optimization approach. A filtering scheme is also adopted to avoid the checkerboard issue and maintain the optimization stability. To present the capability, efficiency and accuracy of the PD-TO approach, various challenging optimization problems with and without defects (cracks) are solved under different boundary conditions. The results are extensively compared and validated with those obtained by element free Galerkin method and FEM. The main advantage of the PD-TO methodology is its ability to handle topology optimization problems of cracked structures without requiring complex treatments for mesh connectivity. Hence, it can be an alternative and powerful tool in finding optimal topologies that can circumvent crack propagation and growth in two and three dimensional structures.",
keywords = "peridynamics, topology optimization, bi-evolutionary structural optimization, cracked structures",
author = "Adnan Kefal and Abdolrasoul Sohouli and Erkan Oterkus and Mehmet Yildiz and Afzal Suleman",
year = "2019",
month = "10",
day = "3",
doi = "10.1007/s00161-019-00830-x",
language = "English",
volume = "21",
pages = "1645--1672",
journal = "Continuum Mechanics and Thermodynamics",
issn = "0935-1175",
number = "6",

}

Topology optimization of cracked structures using peridynamics. / Kefal, Adnan; Sohouli, Abdolrasoul; Oterkus, Erkan; Yildiz, Mehmet; Suleman, Afzal.

In: Continuum Mechanics and Thermodynamics, Vol. 21, No. 6, 30.11.2019, p. 1645-1672.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Topology optimization of cracked structures using peridynamics

AU - Kefal, Adnan

AU - Sohouli, Abdolrasoul

AU - Oterkus, Erkan

AU - Yildiz, Mehmet

AU - Suleman, Afzal

PY - 2019/10/3

Y1 - 2019/10/3

N2 - Finite element method (FEM) is commonly used with topology optimization algorithms to determine optimum topology of load bearing structures. However, it may possess various difficulties and limitations for handling the problems with moving boundaries, large deformations, and cracks/damages. To remove limitations of the mesh-based topology optimization, this study presents a robust and accurate approach based on the innovative coupling of Peridynamics (PD) (a meshless method) and topology optimization (TO), abbreviated as PD-TO. The minimization of compliance, i.e., strain energy, is chosen as the objective function subjected to the volume constraint. The design variable is the relative density defined at each particle employing bi-directional evolutionary optimization approach. A filtering scheme is also adopted to avoid the checkerboard issue and maintain the optimization stability. To present the capability, efficiency and accuracy of the PD-TO approach, various challenging optimization problems with and without defects (cracks) are solved under different boundary conditions. The results are extensively compared and validated with those obtained by element free Galerkin method and FEM. The main advantage of the PD-TO methodology is its ability to handle topology optimization problems of cracked structures without requiring complex treatments for mesh connectivity. Hence, it can be an alternative and powerful tool in finding optimal topologies that can circumvent crack propagation and growth in two and three dimensional structures.

AB - Finite element method (FEM) is commonly used with topology optimization algorithms to determine optimum topology of load bearing structures. However, it may possess various difficulties and limitations for handling the problems with moving boundaries, large deformations, and cracks/damages. To remove limitations of the mesh-based topology optimization, this study presents a robust and accurate approach based on the innovative coupling of Peridynamics (PD) (a meshless method) and topology optimization (TO), abbreviated as PD-TO. The minimization of compliance, i.e., strain energy, is chosen as the objective function subjected to the volume constraint. The design variable is the relative density defined at each particle employing bi-directional evolutionary optimization approach. A filtering scheme is also adopted to avoid the checkerboard issue and maintain the optimization stability. To present the capability, efficiency and accuracy of the PD-TO approach, various challenging optimization problems with and without defects (cracks) are solved under different boundary conditions. The results are extensively compared and validated with those obtained by element free Galerkin method and FEM. The main advantage of the PD-TO methodology is its ability to handle topology optimization problems of cracked structures without requiring complex treatments for mesh connectivity. Hence, it can be an alternative and powerful tool in finding optimal topologies that can circumvent crack propagation and growth in two and three dimensional structures.

KW - peridynamics

KW - topology optimization

KW - bi-evolutionary structural optimization

KW - cracked structures

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

U2 - 10.1007/s00161-019-00830-x

DO - 10.1007/s00161-019-00830-x

M3 - Article

VL - 21

SP - 1645

EP - 1672

JO - Continuum Mechanics and Thermodynamics

T2 - Continuum Mechanics and Thermodynamics

JF - Continuum Mechanics and Thermodynamics

SN - 0935-1175

IS - 6

ER -