Abstract

In this paper the displacement discontinuity method of high-order accuracy and its application to the problems of fracture mechanics are considered. In common practice of applications of boundary element methods, the methods with the piecewise-constant function of boundary displacement are often used. Their advantage against other algorithms is the simplicity of calculation scheme with a rather good accuracy of the solution at the points of region distant from the boundary. In the fracture mechanics (with lines of surfaces of discontinuity of the displacement field), it is required to describe the stress behavior in the proximity of the crack edges with the highest accuracy possible, which leads to necessity of increasing the degree of accuracy of the used numerical methods. It is shown that the methods with high-order continuity of displacements at the boundary proposed in this work substantially improve the accuracy of computation of displacement and stress fields in the neighborhood of crack edges within the region.

中文翻译：

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断裂力学中高阶精度的位移不连续性方法

摘要

本文考虑了高阶位移不连续法及其在断裂力学中的应用。在边界元法应用的常规实践中，经常使用具有边界位移的分段恒定函数的方法。它们相对于其他算法的优势是计算方案简单，并且在远离边界的区域的点处具有很好的求解精度。在断裂力学中（具有位移场的不连续面的线），要求以尽可能高的精度描述裂纹边缘附近的应力行为，这导致必须提高裂纹的精确度。使用数值方法。