Abstract—

The article proposes a numerical method for solving spatial problems of fracture mechanics (method of discontinuous displacements). The advantage of the method is the representation of the solution in the form of a finite series of expansion in terms of the found analytically presented functions. The expansion coefficients are determined from the conditions for fulfilling the boundary conditions in the geometric centers of gravity of the boundary elements. The reliability of the numerical results is shown on test problems for spatial cracks with an analytical solution. The undoubted advantage of the method is the possibility of a mobile solution of the problem for a system of a finite number of cracks with an arbitrary mutual orientation and location in space. The advantage of the method is also a high speed of calculations with satisfactory accuracy, including when calculating stress intensity factors. As a test of the method for a system of cracks, this paper shows the comparison results for the problem of interaction of two cracks, depending on the distance between the planes of the cracks. A comparison is made with a system of two elliptical cracks lying in the same plane. The influence factor (the ratio of the stress intensity factor in the case of a system of cracks to the corresponding value for a single crack) was used as the main characteristic. The comparison with the results of other authors showed good qualitative and quantitative agreement.

中文翻译：

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断裂力学空间问题中不连续位移的数值方法

摘要-

本文提出了一种数值方法来解决断裂力学的空间问题（不连续位移的方法）。该方法的优点是，根据发现的解析表示函数，以有限级数展开形式表示解决方案。根据满足边界条件的边界元素的几何重心中的边界条件的条件来确定膨胀系数。数值结果的可靠性通过解析方法显示在空间裂缝的测试问题上。该方法的毫无疑问的优点是，对于在空间上具有任意相互取向和位置的有限数量的裂纹的系统，该问题的移动解决方案是可能的。该方法的优点还在于包括令人满意的精度在内的高速计算，包括在计算应力强度因子时。作为对裂纹系统方法的测试，本文显示了两个裂纹相互作用问题的比较结果，具体取决于裂纹平面之间的距离。比较了两个位于同一平面上的椭圆形裂纹的系统。主要影响因素是影响因子（在裂纹系统中，应力强度因子与单个裂纹的对应值之比）。与其他作者的结果比较显示出良好的定性和定量一致性。本文根据裂纹平面之间的距离，给出了两个裂纹相互作用问题的比较结果。比较了两个位于同一平面上的椭圆形裂纹的系统。主要影响因素是影响因子（在裂纹系统中，应力强度因子与单个裂纹的对应值之比）。与其他作者的结果比较显示出良好的定性和定量一致性。本文根据裂纹平面之间的距离，给出了两个裂纹相互作用问题的比较结果。比较了两个位于同一平面上的椭圆形裂纹的系统。主要影响因素是影响因子（在裂纹系统中，应力强度因子与单个裂纹的对应值之比）。与其他作者的结果比较显示出良好的定性和定量一致性。主要影响因素是影响因子（在裂纹系统中，应力强度因子与单个裂纹的对应值之比）。与其他作者的结果比较显示出良好的定性和定量一致性。主要影响因素是影响因子（在裂纹系统中，应力强度因子与单个裂纹的对应值之比）。与其他作者的结果比较显示出良好的定性和定量一致性。