A direct traction boundary integral equation method for three-dimension crack problems in infinite and finite domains
A direct traction boundary integral equation method for three-dimension crack problems in infinite and finite domains
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DOI：
10.1007/s00466-013-0918-8
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发表时间：
2014-04
影响因子：
4.1
通讯作者：
G. Xie;Jianming Zhang;Cheng Huang;Chenjun Lu;Guangyao Li
中科院分区：
文献类型：
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作者：
G. Xie;Jianming Zhang;Cheng Huang;Chenjun Lu;Guangyao Li
本文提出了一种求解三维裂纹问题的直接牵引边界积分方程方法。TBIEM是基于牵引边界积分方程（TBIE）。TBIE被配置在两个外部边界和裂纹表面之一。外边界上的位移和力作为未知量，裂纹表面上的相对裂纹张开位移（COD）作为未知量。在我们的实现中，所有的表面被离散成不连续的元素，以满足连续性的要求，有限部分积分的存在，和特殊的裂纹前端元素被构造来捕捉裂纹尖端的行为。为了计算有限部分积分，提出了一种自适应奇异积分技术。应力强度因子（SIF）的计算通过一个修改的COD外推法。数值算例验证了该方法的准确性和有效性。
This paper presents a direct traction boundary integral equation method (TBIEM) for three-dimensional crack problems. The TBIEM is based on the traction boundary integral equation (TBIE). The TBIE is collocated on both the external boundary and one of the crack surfaces. The displacements and tractions are used as unknowns on the external boundary and the relative crack opening displacements (CODs) are introduced as unknowns on the crack surface. In our implementation, all the surfaces of the considered structure are discretized into discontinuous elements to satisfy the continuity requirement for the existence of finite-part integrals, and special crack-front elements are constructed to capture the crack-tip behavior. To calculate the finite-part integrals, an adaptive singular integral technique is proposed. The stress intensity factors (SIFs) are computed through a modified COD extrapolation method. Numerical examples of SIFs computation are presented to demonstrate the accuracy and efficiency of our method.