最小二乘和奇异值分解法在边界元法中的应用

采用最小二乘与奇异值分解结合的方法，给出求解系数矩阵不满秩的线性代数方程组的数值方法，进而将此方法应用于边界无法中，处理给定外力的第一边值问题，特别地用于处理给定外力的三维裂纹问题。此外，本文还给出求解三维有限体裂纹问题的超奇异积分方程组，并使用有限部积分与边界元法为其建立了数值法。最后计算了若于典型例子的应力强度因子，数值结果与现有文献的相比，符合很好。

Application of Least Squares and Singular Value Resolving Method to Boundary Element Method

The application of least squares and singular value resolving method to linear algebraic equations is introduced. This method is very effective to the algebraic equations whose matrix is singular. It may be applied to the boundary element method which treats the elasticity problems with the conditions of given external loadings, specifically to planar crack problems in three dimensional elasticity. Moreover, the hypersingular integral equations of a planar crack embedded in a 3-D finite body are given, and the finite-part integral and boundary element method is used to discretize the equations as a set of linear algebraic equations which are solved by the least squares and singular value resolving method. Finally several typical examples are calculated, and the numerical results of the stress intensity factors are obtained.