求解三维裂纹前缘SIF分布时间历程的通用权函数法和有限变分法

将三维热权函数法扩展为适用于表面力、体积力和温度载荷的通用权函数法(UWF).推导出以变分型积分方程表达的UWF法基本方程,从变分的角度,将求解三维热权函数法基本方程的多虚拟裂纹扩展法(MVCE)改造为可以适用于一般的变分型积分方程的一类新型数值方法--有限变分法(FVM).在FVM中可以引入无穷多种线性无关的局部变分模式,可以根据计算要求在求解域中插入任意多个计算节点,单一型裂纹问题FVM所得到的最终方程组的系数矩阵总是一个对称的窄带矩阵,而且对角元总是大数,具有良好的数值计算性能.FVM对于SIF沿裂纹前缘急剧变化的复杂情况具有较好的数值模拟能力和较高的计算精度,利用自身一致性,可以求得三维裂纹前缘SIF的高精度解.

General Weight Function and Finite Variation for Determination SIF Distribution History Along 3-D Crack Fronts

3-D thermal weight function (TWF) method was extended to the general weight function (GWF) method for solving the problems of cracked bodies subjected to surface tractions, volume forces and thermal loadings. The basic equation for GWF method was expressed by a variational integral equation. The multiple virtual crack extension (MVCE) method for solving the 3-D TWF equations was developed to a new numerical procedure, finite variation method (FVM), which gets suitable to the general variational integral equations. In FVM, unlimited linearly independent local variation modes is introduced, and any amount of nodes can be inserted in the variation domain. The coefficient matrix of the final equations for single mode crack problems is always a symmetrical matrix with small bandwidth and major diagonals. The complex situations for dramatically varied SIFs along crack fronts are numerically simulated, with higher accuracy.