含内裂纹的有限圆盘的平面问题

本文用弹性理论复变函数方法讨论了在内部任意位置含直线裂纹的有限圆盘在一般载荷作用下的平面问题,得到了复应力函数和应力强度因子用级数表示的一般表达式,并对此问题讨论了三种特殊情形,即裂纹受均布压应力,均布剪应力和圆盘匀速旋转的情形,其中还给出了计算应力强度因子的近似式.计算结果表明,对位于圆盘内部且不靠近外边界的中、小裂纹,这些近似式给出好的或较好的近似.

Plane Problems of a Finite Disc Containing an Internal Crack

Using complex variable methods in elasticity, this paper deals with the plane problems of a finite disc containing an internal linear crack at any position under general loads, obtains the general forms of complex stress functions an dstress-inten-sity factors, expressed in terms of series, and to these problems discusses three special cases, i. e. the cases of the crack under a uniform pressure, a uniform shear stress and the case of the disc rotating uniformly. In these cases the approximate formulas calculating the stress-intensity factors are also presented. The calculated results show that for the middle and small cracks situated inside the disc and not near the external boundary, these approximate formulas give good or better approx- imation.