Analysis of Cracked Plates Using Localized Multi-Domain Differential Quadrature Method

Tharwat Osman; Mohamed. S. Matbuly; Salwa. A. Mohamed; Mohamed Nassar

doi:doi:10.11648/j.acm.20130204.12

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Analysis of Cracked Plates Using Localized Multi-Domain Differential Quadrature Method

Tharwat Osman, Mohamed. S. Matbuly, Salwa. A. Mohamed, Mohamed Nassar

Published in Applied and Computational Mathematics (Volume 2, Issue 4)

Received: 5 August 2013 Accepted: Published: 30 August 2013

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Abstract

In this paper, A multi-domain differential quadrature method is employed to solve a mode III crack problem. The domain of the problem is assumed to be irregular rather than it possesses discontinuities, (cracks). The entire domain is divided into several subdomains, according to the crack locations. A conformal mapping is applied to transform the irregular subdomains to regular ones. Then the differential quadrature method is employed to solve the problem over the transformed domains. Further, it’s focused on the crack regions by applying the localized version of differential quadrature method. The out of plane deflection is obtained at the immediate vicinity of the crack tips, such that the stress intensity factor can be calculated. The obtained results are compared with the previous analytical ones. Furthermore a parametric study is introduced to investigate the effects of elastic and geometric characteristics on the values of stress intensity factor.

Published in	Applied and Computational Mathematics (Volume 2, Issue 4)
DOI	10.11648/j.acm.20130204.12
Page(s)	109-114
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Irregular, Localized Differential Quadrature, Conformal Mapping, Mode III, Stress Intensity Factor

References

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APA Style

Tharwat Osman, Mohamed. S. Matbuly, Salwa. A. Mohamed, Mohamed Nassar. (2013). Analysis of Cracked Plates Using Localized Multi-Domain Differential Quadrature Method. Applied and Computational Mathematics, 2(4), 109-114. https://doi.org/10.11648/j.acm.20130204.12

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ACS Style

Tharwat Osman; Mohamed. S. Matbuly; Salwa. A. Mohamed; Mohamed Nassar. Analysis of Cracked Plates Using Localized Multi-Domain Differential Quadrature Method. Appl. Comput. Math. 2013, 2(4), 109-114. doi: 10.11648/j.acm.20130204.12

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AMA Style

Tharwat Osman, Mohamed. S. Matbuly, Salwa. A. Mohamed, Mohamed Nassar. Analysis of Cracked Plates Using Localized Multi-Domain Differential Quadrature Method. Appl Comput Math. 2013;2(4):109-114. doi: 10.11648/j.acm.20130204.12

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@article{10.11648/j.acm.20130204.12,
  author = {Tharwat Osman and Mohamed. S. Matbuly and Salwa. A. Mohamed and Mohamed Nassar},
  title = {Analysis of Cracked Plates Using Localized Multi-Domain Differential Quadrature Method},
  journal = {Applied and Computational Mathematics},
  volume = {2},
  number = {4},
  pages = {109-114},
  doi = {10.11648/j.acm.20130204.12},
  url = {https://doi.org/10.11648/j.acm.20130204.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20130204.12},
  abstract = {In this paper, A multi-domain differential quadrature method is employed to solve a mode III crack problem. The domain of the problem is assumed to be irregular rather than it possesses discontinuities, (cracks). The entire domain is divided into several subdomains, according to the crack locations. A conformal mapping is applied to transform the irregular subdomains to regular ones. Then the differential quadrature method is employed to solve the problem over the transformed domains. Further, it’s focused on the crack regions by applying the localized version of differential quadrature method. The out of plane deflection is obtained at the immediate vicinity of the crack tips, such that the stress intensity factor can be calculated. The obtained results are compared with the previous analytical ones. Furthermore a parametric study is introduced to investigate the effects of elastic and geometric characteristics on the values of stress intensity factor.},
 year = {2013}
}

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TY - JOUR
T1 - Analysis of Cracked Plates Using Localized Multi-Domain Differential Quadrature Method
AU - Tharwat Osman
AU - Mohamed. S. Matbuly
AU - Salwa. A. Mohamed
AU - Mohamed Nassar
Y1 - 2013/08/30
PY - 2013
N1 - https://doi.org/10.11648/j.acm.20130204.12
DO - 10.11648/j.acm.20130204.12
T2 - Applied and Computational Mathematics
JF - Applied and Computational Mathematics
JO - Applied and Computational Mathematics
SP - 109
EP - 114
PB - Science Publishing Group
SN - 2328-5613
UR - https://doi.org/10.11648/j.acm.20130204.12
AB - In this paper, A multi-domain differential quadrature method is employed to solve a mode III crack problem. The domain of the problem is assumed to be irregular rather than it possesses discontinuities, (cracks). The entire domain is divided into several subdomains, according to the crack locations. A conformal mapping is applied to transform the irregular subdomains to regular ones. Then the differential quadrature method is employed to solve the problem over the transformed domains. Further, it’s focused on the crack regions by applying the localized version of differential quadrature method. The out of plane deflection is obtained at the immediate vicinity of the crack tips, such that the stress intensity factor can be calculated. The obtained results are compared with the previous analytical ones. Furthermore a parametric study is introduced to investigate the effects of elastic and geometric characteristics on the values of stress intensity factor.
VL - 2
IS - 4
ER -

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Author Information

Tharwat Osman

Dept. of Math. And Phys., Faculty of Engineering, Zagazig University, Zagazig, Egypt
Mohamed. S. Matbuly

Dept. of Math. And Phys., Faculty of Engineering, Zagazig University, Zagazig, Egypt
Salwa. A. Mohamed

Dept. of Math. And Phys., Faculty of Engineering, Zagazig University, Zagazig, Egypt
Mohamed Nassar

Dept. of Math. And Phys., Faculty of Engineering, Cairo University, Giza, Egypt

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Plain Text BibTeX RIS

APA Style

Tharwat Osman, Mohamed. S. Matbuly, Salwa. A. Mohamed, Mohamed Nassar. (2013). Analysis of Cracked Plates Using Localized Multi-Domain Differential Quadrature Method. Applied and Computational Mathematics, 2(4), 109-114. https://doi.org/10.11648/j.acm.20130204.12

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ACS Style

Tharwat Osman; Mohamed. S. Matbuly; Salwa. A. Mohamed; Mohamed Nassar. Analysis of Cracked Plates Using Localized Multi-Domain Differential Quadrature Method. Appl. Comput. Math. 2013, 2(4), 109-114. doi: 10.11648/j.acm.20130204.12

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AMA Style

Tharwat Osman, Mohamed. S. Matbuly, Salwa. A. Mohamed, Mohamed Nassar. Analysis of Cracked Plates Using Localized Multi-Domain Differential Quadrature Method. Appl Comput Math. 2013;2(4):109-114. doi: 10.11648/j.acm.20130204.12

Copy | Download

@article{10.11648/j.acm.20130204.12,
  author = {Tharwat Osman and Mohamed. S. Matbuly and Salwa. A. Mohamed and Mohamed Nassar},
  title = {Analysis of Cracked Plates Using Localized Multi-Domain Differential Quadrature Method},
  journal = {Applied and Computational Mathematics},
  volume = {2},
  number = {4},
  pages = {109-114},
  doi = {10.11648/j.acm.20130204.12},
  url = {https://doi.org/10.11648/j.acm.20130204.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20130204.12},
  abstract = {In this paper, A multi-domain differential quadrature method is employed to solve a mode III crack problem. The domain of the problem is assumed to be irregular rather than it possesses discontinuities, (cracks). The entire domain is divided into several subdomains, according to the crack locations. A conformal mapping is applied to transform the irregular subdomains to regular ones. Then the differential quadrature method is employed to solve the problem over the transformed domains. Further, it’s focused on the crack regions by applying the localized version of differential quadrature method. The out of plane deflection is obtained at the immediate vicinity of the crack tips, such that the stress intensity factor can be calculated. The obtained results are compared with the previous analytical ones. Furthermore a parametric study is introduced to investigate the effects of elastic and geometric characteristics on the values of stress intensity factor.},
 year = {2013}
}

Copy | Download