有限体三维断裂的奇异积分方程组(英文)

复杂有限体的工程实践中常出现不只是椭圆形的各种形状空间裂缝，需要确定它们是否会扩展并给建筑物带来危险。文中通过Ｈａｎｋｅｌ变换给出单位集中位错引起弹性体中的应力位移场的基本方程，沿工程结构外边界和复杂空间裂缝表面的虚分布位错建立奇异积分方程组应满足已知边界条件。这些分布位错的解将直接得出各方向的应力强度因子及有限域的应力和位移场。以典型的椭圆裂缝作为简单数值示例来检验精度表明，该法所用计算时间较少并和理论解吻合良好。该法已用于老结构物的缺陷维修工程。

Singular Integral Equation Groups for 3-D Crack Problems in Finite Body

Various shapes of space cracks (not only elliptical) always happen in engineering practice (finite complicated body). It is necessary to determine whether they will propagate and bring danger to the structure. In present paper, the fundamental equations of stressdisplacement field in elastic body due to unit concentrated dislocation are given through Hankel transform. Singular integral equation groups caused by fictitious distributed dislocation along the outer boundaries of engineering structure and complicated space crack surface are constructed to satisfy the known boundary conditions. Solutions of these distributed dislocations will directly give the SIF (stress intensity factor ) of the crack in various directions, the stress and displacement field of finite body. Simple numerical example of typical elliptical crack is used for precision check, which shows results in good agreement with theoretical result and with less computing time of the present method. The present method has been used for the repairment of the defects in old structure.