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

Received: 5 August 2013     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), 2013. Published by Science Publishing Group

Keywords

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

References
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Cite This Article
  • 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
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    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
  • Dept. of Math. And Phys., Faculty of Engineering, Zagazig University, Zagazig, Egypt

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

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

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

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