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首页> 外文期刊>The Journal of Strain Analysis for Engineering Design >Multiple-crack analysis with the quasi-higher-order symmetric Galerkin boundary element method
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Multiple-crack analysis with the quasi-higher-order symmetric Galerkin boundary element method

机译：准高阶对称Galerkin边界元方法的多裂纹分析

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摘要

This paper describes the application of the symmetric Galerkin boundary element method (SGBEM) for the analysis of a two-dimensional linear elastic crack problem. The direct SGBEM for the multiple-crack problem is derived using the Betti reciprocal theorem, resulting in a completely symmetric matrix. The auxiliary fictitious state is used to obtain the equations. This approach can deal with any number of traction-free cracks within a single domain. Two-stage interpolation method called the 'quasi-higher-order element method' (QHOEM) is then proposed to solve the double integrals. In the initial stage, it uses higher-order elements to interpolate the field variables and, for the numerical integration involved, it further uses interpolation functions to decompose the higher-order elements into lower-order elements so that the existing analytical integration can be applied. Thus, it can be embedded into the present codes with ease and also reduces the computational cost. A finite rectangular plate containing a slanting crack and a kinked crack has been analysed to check the accuracy of the proposed method. A load-carrying fillet welded joint containing several cracks is then analysed, and the stress intensity factors at the crack tips are found to be in complete agreement with the dual-boundary-element method results.
机译：本文介绍了对称Galerkin边界元方法（SGBEM）在二维线性弹性裂纹问题分析中的应用。使用贝蒂互易定理推导用于多裂纹问题的直接SGBEM，得到一个完全对称的矩阵。辅助虚拟状态用于获得方程式。这种方法可以处理单个域内的任意数量的无牵引裂纹。然后提出了两级插值方法，称为“拟高阶元素方法”（QHOEM），以解决双重积分问题。在初始阶段，它使用高阶元素对字段变量进行插值，并且对于所涉及的数值积分，还使用插值函数将高阶元素分解为低阶元素，从而可以应用现有的分析积分。因此，可以容易地将其嵌入到当前代码中，并且还降低了计算成本。分析了包含倾斜裂纹和扭折裂纹的有限矩形板，以检验所提方法的准确性。然后分析了包含多个裂纹的载重角焊缝，发现裂纹尖端的应力强度因子与双边界元法结果完全一致。

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