Abstract In this paper, a functionally graded (FG) hollow cylinder with fully multiple longitudinal cracks is analyzed using the weight function method (WFM). The cylinder's inner surface is made of Al2O3, while the outer surface is made of TiC. The distribution of material properties is continuously due to the power-law function. The cracks placed in such a way to have identical angles relative to each other. At first, to extract the WF, the stress intensity factors (SIFs) are determined based on the reference loadings on the crack surface using two-dimensional finite element (FE) modelling, considering the effect of changing elasticity modulus and Poisson's ratio. Then, by fitting the curve to the results, the unknown coefficients of the WF are extracted as a function of four parameters, i.e., the crack relative depth, the non-homogeneity coefficient of FG material, the radius ratio of cylinder, and the number of cracks. The results obtained from WFM are compared to those in the literature and FE data in special cases of loading, confirming the high accuracy of the WF. Finally, a pressurized FG hollow cylinder is analyzed using WFM for various sets of parameters.

中文翻译：

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功能梯度空心圆柱体中多个纵向裂纹的权重函数

摘要 本文采用权函数法(WFM)分析了一个具有完全多重纵向裂纹的功能梯度(FG)空心圆柱体。圆柱体的内表面由 Al2O3 制成，而外表面由 TiC 制成。由于幂律函数，材料特性的分布是连续的。裂缝以相对于彼此具有相同角度的方式放置。首先，为了提取 WF，考虑到弹性模量和泊松比变化的影响，使用二维有限元 (FE) 建模基于裂纹表面上的参考载荷确定应力强度因子 (SIF)。然后，通过对结果进行曲线拟合，提取 WF 的未知系数作为四个参数的函数，即裂缝相对深度，FG 材料的非均质系数、圆柱半径比和裂纹数量。将 WFM 获得的结果与文献中的结果和特殊加载情况下的有限元数据进行了比较，证实了 WF 的高精度。最后，使用 WFM 分析加压 FG 空心圆柱体的各种参数集。