Mixed mode BEM analysis of multiple curvilinear cracks in the general anisotropic solids by the crack tip singular element
Mixed mode BEM analysis of multiple curvilinear cracks in the general anisotropic solids by the crack tip singular element
复制标题
一般各向异性固体中多重曲线裂纹的裂纹尖端奇异元混合模式边界元分析
DOI：
10.1016/j.ijsolstr.2003.11.005
复制
发表时间：
2004
影响因子：
3.6
通讯作者：
María E. Marante
中科院分区：
文献类型：
--
作者：
M. Denda;María E. Marante
本文考虑二维一般各向异性固体中的多曲线裂纹，建立了一种计算有效的方法来精确地确定应力强度因子。每个曲线裂纹由一组直裂纹单元表示，裂纹张开位移（COD）由位错偶极子的连续分布表示。位于裂纹尖端旁边的裂纹单元称为裂纹尖端奇异单元（CTSE），其中已知的r裂纹尖端张开位移和1/ r应力奇异性在使用Chebyshev多项式的COD的插值中数学地建立。远离裂纹尖端的规则裂纹单元采用二次多项式插值。简单的解析公式的位移，牵引力，和应力强度因子（SIF）的贡献CTSE开发在其自己的COD系数。由于SIF是在主处理过程中获得的，因此不需要后处理;这与强大的四分之一点元素相比具有明显的优势。几个多曲线裂纹问题的数值结果表明，该技术的准确性和简单性。
We consider multiple curvilinear cracks in the two-dimensional general anisotropic solids and establish a computationally effective technique to determine the stress intensity factors accurately. Each curvilinear crack is represented by a collection of straight crack elements and the crack opening displacement (COD) by the continuous distribution of the dislocation dipoles. The crack element located next to the crack tip is called the crack tip singular element (CTSE), where the known r crack tip opening displacement and the 1/ r stress singularity is mathematically built in the interpolation of the COD using the Chebyshev polynomials. The regular crack elements away from the crack tip use the quadratic polynomial interpolation for the CODs. Simple analytical formulas for the displacement, traction, and the stress intensity factor (SIF) contributions for the CTSE are developed in terms of its own COD coefficients. Since the SIFs are obtained during the main processing no post processing is required; a distinct advantage over the powerful quarter-point element. Numerical results are given for several multiple curvilinear crack problems to demonstrate the accuracy and simplicity of the technique.