Volume 14, Issue 6
Numerical Analysis of Crack-Tip Fields Using a Meshless Method in Linear Elastic Materials

Adv. Appl. Math. Mech., 14 (2022), pp. 1509-1534.

Published online: 2022-08

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• Abstract

In this paper, the Discrete Least Squares Meshless (DLSM) method is developed to determine crack-tip fields. In DLSM, the problem domain and its boundary are discretized by unrelated field nodes used to introduce the shape functions by the moving least-squares (MLS) interpolant. This method aims to minimize the sum of squared residuals of the governing differential equations at any nodal point. Since high-continuity shape functions are used, some necessary treatments, including the visibility criterion, diffraction, and transparency approaches, are employed in the DLSM to introduce strong discontinuities such as cracks. The stress extrapolation and $J$-integral methods are used to calculate stress intensity factors. Three classic numerical examples using three approaches to defining discontinuities in the irregular distribution of nodal points are considered to investigate the effectiveness of the DLSM method. The numerical tests indicated that the proposed method effectively employed the approaches to defining discontinuities to deal with discontinuous boundaries. It was also demonstrated that the diffraction approach obtained higher accuracy than the other techniques.

• Keywords

Numerical analysis, partial differential equations, fracture mechanics, meshless method, discrete least-squares, modification of weight function, approaches to defining discontinuities, stress intensity factors.

74A45, 65N22, 74S99

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@Article{AAMM-14-1509, author = {Zahra and Sheikhi and and 24255 and and Zahra Sheikhi and Akbar and Ghanbari and and 24256 and and Akbar Ghanbari and Mohammad and Karkon and and 24257 and and Mohammad Karkon and Soleyman and Ghouhestani and and 24258 and and Soleyman Ghouhestani}, title = {Numerical Analysis of Crack-Tip Fields Using a Meshless Method in Linear Elastic Materials}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {14}, number = {6}, pages = {1509--1534}, abstract = {

In this paper, the Discrete Least Squares Meshless (DLSM) method is developed to determine crack-tip fields. In DLSM, the problem domain and its boundary are discretized by unrelated field nodes used to introduce the shape functions by the moving least-squares (MLS) interpolant. This method aims to minimize the sum of squared residuals of the governing differential equations at any nodal point. Since high-continuity shape functions are used, some necessary treatments, including the visibility criterion, diffraction, and transparency approaches, are employed in the DLSM to introduce strong discontinuities such as cracks. The stress extrapolation and $J$-integral methods are used to calculate stress intensity factors. Three classic numerical examples using three approaches to defining discontinuities in the irregular distribution of nodal points are considered to investigate the effectiveness of the DLSM method. The numerical tests indicated that the proposed method effectively employed the approaches to defining discontinuities to deal with discontinuous boundaries. It was also demonstrated that the diffraction approach obtained higher accuracy than the other techniques.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2021-0058}, url = {http://global-sci.org/intro/article_detail/aamm/20857.html} }
TY - JOUR T1 - Numerical Analysis of Crack-Tip Fields Using a Meshless Method in Linear Elastic Materials AU - Sheikhi , Zahra AU - Ghanbari , Akbar AU - Karkon , Mohammad AU - Ghouhestani , Soleyman JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1509 EP - 1534 PY - 2022 DA - 2022/08 SN - 14 DO - http://doi.org/10.4208/aamm.OA-2021-0058 UR - https://global-sci.org/intro/article_detail/aamm/20857.html KW - Numerical analysis, partial differential equations, fracture mechanics, meshless method, discrete least-squares, modification of weight function, approaches to defining discontinuities, stress intensity factors. AB -

In this paper, the Discrete Least Squares Meshless (DLSM) method is developed to determine crack-tip fields. In DLSM, the problem domain and its boundary are discretized by unrelated field nodes used to introduce the shape functions by the moving least-squares (MLS) interpolant. This method aims to minimize the sum of squared residuals of the governing differential equations at any nodal point. Since high-continuity shape functions are used, some necessary treatments, including the visibility criterion, diffraction, and transparency approaches, are employed in the DLSM to introduce strong discontinuities such as cracks. The stress extrapolation and $J$-integral methods are used to calculate stress intensity factors. Three classic numerical examples using three approaches to defining discontinuities in the irregular distribution of nodal points are considered to investigate the effectiveness of the DLSM method. The numerical tests indicated that the proposed method effectively employed the approaches to defining discontinuities to deal with discontinuous boundaries. It was also demonstrated that the diffraction approach obtained higher accuracy than the other techniques.

Zahra Sheikhi, Akbar Ghanbari, Mohammad Karkon & Soleyman Ghouhestani. (2022). Numerical Analysis of Crack-Tip Fields Using a Meshless Method in Linear Elastic Materials. Advances in Applied Mathematics and Mechanics. 14 (6). 1509-1534. doi:10.4208/aamm.OA-2021-0058
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