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 - <p style="text-align: justify;">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.</p>