多裂纹问题计算分析的本征COD边界积分方程方法

针对多裂纹问题,若采用常规的数值求解技术,计算效率较低.为实现多裂纹问题的大规模数值模拟,建立了本征裂纹张开位移(crack opening displacement,COD)边界积分方程及其迭代算法,并引入Eshelby矩阵的定义,将多裂纹分为近场裂纹和远场裂纹来处理裂纹间的相互影响.以采用常单元作为离散单元的快速多极边界元法为参照,对提出的计算模型和迭代算法进行了数值验证.结果表明,本征COD边界积分方程方法在处理多裂纹问题时取得较大的改进,其计算效率显著高于传统的边界元法和快速多极边界元法.

Analysis of Multicrack Problems With Eigen COD Boundary Integral Equations

For multicrack problems, the conventional numerical solution techniques are of low efficiency. To realize large-scale numerical simulation of multicrack problems, the eigen crack opening displacement (COD) boundary integral equations and the pertinent iteration algorithm were established. To deal with the interactions between cracks, the local Eshelby matrix was introduced. In this way, the superposition technique was employed with all cracks divided into 2 groups, i.e. the adjacent group and the far-field group, according to a non-dimensional radial distance of a crack to the current crack. In comparison to the fast multipole boundary element method with a constant element as the discrete element, the proposed computational model and the iteration algorithm were numerically verified. The numerical results show that, the model for the eigen COD boundary integral equations gets great improvement in dealing with multicrack problems, and its computation efficiency is significantly higher than those of the traditional boundary element method and the fast multipole boundary element method.