Open Access


Download data is not yet available.


This paper investigates the fracture behavior of plates with through-thickness crack by using the extended concept of the Radial Point Interpolation Method (RPIM). The attractiveness of the RPIM shape functions is the satisfaction of the Kronecker delta property providing direct imposition of essential boundary conditions. In the extended concept, the jump in deflection and rotation fields caused by crack, also the stress singularity near the crack tip are described by adding enriched functions to the interpolation equation. Particularly, Heaviside function and asymptotic enriched function. For numerical integration, the Cartesian Transformation Method (CTM) is employed. No integration background cell is required in CTM, this technique transforms a domain integral into a boundary integral and a 1D integral. For analysis of discontinuous problems, in this study, the distribution of integration points is manipulated to avoid the discontinuity caused by crack segmentation. Therefore, no subdomains are required, unlike other reference CTM studies. To achieve that, a virtual boundary is introduced that represents the discontinuity such as holes or cracks. This also matches the concept of the extended approach that no explicit discontinuity exists in the geometry, instead, the discontinuity is modelled by mathematics equation. The Stress Intensity Factors (SIFs) of the cracked plate are evaluated through the interaction integral technique. The efficiency of the proposed method is illustrated through various numerical examples. The accuracy of the obtained results are compared with other available numerical solutions and analytical solutions.

Author's Affiliation
  • Vay Siu Lo

    Google Scholar Pubmed

  • Hien Thai Nguyen

    Google Scholar Pubmed

  • Tich Thien Truong

    Google Scholar Pubmed

  • Nha Thanh Nguyen

    Email I'd for correspondance:
    Google Scholar Pubmed

Article Details

 Copyright Info

Creative Commons License

Copyright: The Authors. This is an open access article distributed under the terms of the Creative Commons Attribution License CC-BY 4.0., which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding data

 How to Cite
Lo, V. S., Nguyen, H. T., Truong, T. T., & Nguyen, N. (2023). Crack Analysis by Using An Extended Meshfree Method and Cartesian Transformation Method without Creating Subdomains. VNUHCM Journal of Engineering and Technology, 5(SI2), 33-43.

 Cited by

Article level Metrics by Paperbuzz/Impactstory
Article level Metrics by Altmetrics

 Article Statistics
HTML = 1024 times
PDF   = 258 times
Total   = 258 times