含内裂纹的有限圆盘的平面问题
Plane Problems of a Finite Disc Containing an Internal Crack
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摘要: 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.Abstract: Using complex variable methods in elasticity, this paper deals with the plane problems ot a finite disc containing an internal linear crack at any position under general loads, obtains the general forms of Complex stress functions and stress-intensity tactors expressed in terms of series, and to these problems disiusses three sposial cases,i.e.the cases of the crack under a uniform pressure, a uniform shear stress and the use of the dise rotating uniformly. In these cases the approximate formulas calcidating the stress-intensity factors are also presented. The calculated results shun that for the middle and.small orachs situated inside the disc and not near the external boundary,these approximate formulas give good or better approximation.
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Key words:
- plane problem /
- disc containing a crack /
- stress-intensity factor /
- stress field /
- displacement field
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[1] Tada,H.,P.C.Paris and G.R.Irwin,The Stress Analysis of Cracks Handbook,Del Research Corporation.Hellertown Pennsyvania(1973). [2] Bowie.O.L.and D.M.Neal.A modified mapping-collocation technique for accurate calculation of stress intensity factors.Int.J.Fract.Mech.,6(1970),199-206. [3] Tweed,J.,S.C.Das and D.P.Rooke,The stress intensity factors of a radial crack in a finite elastic disc,Int.J.Engng.Sci.,10(1972).323-335. [4] Rooke,D.P.and J.Tweed,The stress intensity factors of a radial crack in a finite rotating elastic disc,Int.J.Engng.Sci.10(1972).709-714. [5] 汤任基、蒋柱中,有限圆板上的径向裂纹系分析,固体力学学报,4(1881),445-458 [6] Panasyuk,V.V.,M.P.Sayruk and A.P.Datsyshyn.A general method of solution of twodimensional problems in the theory of cracks.Engng.Fract.Mech.,9(1977),481-497. [7] Muskhelishvili,N.I.,Some Basic Problems of the Mathematical Theory of Elasticily,Noordhoff(1963). [8] 尹昌言,有穿透裂纹的圆柱体扭转应力及应力强度因子,固体力学学报,3(1982),393-405 [9] 尹昌言、祖承德,含裂纹的圆柱体的弯曲,应用数学和力学,8,11(1987),1015-1026. -
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