An improvement for the extended integrated radial basis functions (XiRBF) meshfree method is proposed in this study for dynamic crack analysis in bending plate structure. The deformation behavior of plate structure is described by the first-order shear deformation theory (FSDT). The iRBF approach offers a benefit by commencing the approximation procedure with the primary function’s highest-order derivative and subsequently deriving lower-order derivatives through integration. This method of approximation has the potential to provide more precise results for derivative values that frequently appear in the governing equations of boundary value problems. With the proposed improvement in iRBF, the matrix is turned into a square matrix so that it is invertible, the approach is now more stable even for irregularly distributed nodes, and the number of nodes in each support domain can be arbitrary. Furthermore, the iRBF shape function possesses the Kronecker delta property, enabling the straightforward application of essential boundary conditions similar to the finite element method. In the analysis of fractures, the Heaviside function is employed to depict the discontinuous characteristics of crack surfaces. Additionally, to account for the singularity at the crack tip, enriched functions are appropriately chosen, guided by asymptotic analysis derived from the analytical solution. Several numerical tests are conducted to calculate dynamic stress resultant intensity factors (DSRIFs) in bending plate problems. The accuracy and efficiency of the suggested method are validated by comparing the obtained results with those from other existing solutions.

中文翻译：

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改进的扩展积分径向基函数无网格方法用于弯板结构动态断裂分析


本研究提出了一种对扩展积分径向基函数（XiRBF）无网格方法的改进，用于弯板结构的动态裂纹分析。板结构的变形行为由一阶剪切变形理论（FSDT）描述。 iRBF 方法的优点是，以主函数的最高阶导数开始近似过程，然后通过积分导出低阶导数。这种近似方法有可能为边值问题控制方程中经常出现的导数值提供更精确的结果。通过对 iRBF 的改进，矩阵变成了方阵，使其可逆，即使对于不规则分布的节点，该方法现在也更加稳定，并且每个支持域中的节点数量可以是任意的。此外，iRBF 形函数具有 Kronecker delta 属性，可以像有限元方法一样直接应用基本边界条件。在断裂分析中，采用Heaviside函数来描述裂纹表面的不连续特征。此外，为了解释裂纹尖端的奇异性，在从解析解导出的渐近分析的指导下，适当选择丰富的函数。进行了多项数值测试来计算弯曲板问题中的动应力合成强度因子 (DSRIF)。通过将获得的结果与其他现有解决方案的结果进行比较，验证了所建议方法的准确性和效率。