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Analysis of 3D Planar Crack Problems by Body Force Method

机译:用体力法分析三维平面裂纹问题

摘要

Derivation of the integral equation for general 3D crack problems was examined based on the theory of body force method. In the present analysis, stress intensity factors (SIFs) along a front of arbitrary shaped 3D planar crack are obtained directly only by solving simultaneous equations expressing a boundary condition. The crack surface is discretized using number of triangular elements and the variation of the force doublet embedded in each triangle is assumed at constant. The derived boundary integral equation was transformed into a set of simultaneous equations and was solved computationally. In order to improve the accuracy of the numerically examined boundary integral, a polar transformation scheme combined with Tayler expansion of the fundamental solutions is introduced. Not only a single crack problem but also an interference among coplanar cracks can be calculated using the unique program developed in this research. It was verified that as the number of triangular elements increases, the evaluated SIF converges to the reference solution.
机译:基于体力法理论,研究了一般3D裂纹问题的积分方程的推导。在目前的分析中,仅通过求解表示边界条件的联立方程,即可直接获得沿任意形状的3D平面裂纹前面的应力强度因子(SIF)。使用三角形元素的数量来离散裂纹表面,并且假定每个三角形中嵌入的力双峰的变化是恒定的。将导出的边界积分方程转换为一组联立方程,并通过计算进行求解。为了提高数值检验边界积分的准确性,引入了结合基本解的泰勒展开的极坐标变换方案。使用本研究开发的独特程序,不仅可以计算单个裂纹问题,而且可以计算共面裂纹之间的干扰。证实随着三角形元素数量的增加,评估的SIF收敛到参考解。

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