圆盘状Ⅰ型裂纹的非局部理论解

SOLUTION OF THE NONLOCAL THEORY OF DISK CRACK OF TYPE I

本文采用非局部弹性理论研究了三维圆盘状Ⅰ型裂纹问题。给出了轴对称问题的影响函数，导出了圆盘状Ⅰ型裂纹非局部理论解的对偶积分方程。对具有无界核积分方程的求解问题提出了一种有效的解决方法，使无界核问题转化为有界核问题。给出了圆盘状Ⅰ型裂纹问题裂纹尖端应力场的数值解，结果表明，非局部理论消除了本文三维问题裂纹尖端应力场的奇异性，文中还对裂纹尖端应力场的大小和分布等进行了研究。

A three-dimensional problem of disk crack of type I is studied according to the theory of nonlocal elasticity in this paper.The influence function of the axisymmetrical problem is given,and dual integral equations of the problem are derived.An effective method is devised to deal with the nitegral equation of unbounded kernels by changing the unbounded kernel into bounded ones.The nUmerical solution of stress field at the adge of disk crack is presented,it is found that no stress singularity is present at the acrck tip.The.;value and distribution of stresses at.the crack tip are also studied in the paper.