三维有限体平片裂纹的超奇异积分方程与边界元法

HYPERSINGULAR INTEGRAL EQUATIONS AND BOUNDARY ELEMENT METHOD FOR PLANAR CRACK PROBLEMS IN THREE DIMENSIONAL FINITE BODIES

利用Ｓｏｍｉｇｌｉａｎａ公式及有限部积分的概念，导出了含任意平片裂纹三维有限体问题的超奇异积分方程组，并联合使用有限部积分与边界元法，建立了数值求解方法．在裂纹前沿附近单元，采用与理论分析一致的平方根位移模型，以提高数值结果的精度．最后计算了若干典型例子的应力强度因子．

Using the Somigliana representation and the concepts of finite part integrals, a set of hypersingular integral equations of a planar crack in a three dimensional finite body and subjected to arbitrary loads are derived,and a numerical method is proposed by combining the finite part integral method with the boundary element method. According to the analytic theory of hypersingular integral equations, the square root models of displacement discontinuities in the elements near the crack front are applied, and thus the computing precision is raised. Finally, the stress intensity factors of several typical planar crack problems are calculated.