含裂纹的圆柱体的弯曲

尹昌言; 祖承德

含裂纹的圆柱体的弯曲

尹昌言¹,
祖承德²

1.
洛阳工学院;
2.
东北重型机械学院

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出版历程
- 收稿日期: 1985-12-15
- 刊出日期: 1987-11-15

Bending of a Circular Cylinder Containing a Crack

Yin Chang-yan¹,
Zu Cheng-de²

1.
Luoyang Institute of Technology. Luoyang;
2.
The North-East Heary Machinery Institute, Qiqihaer

摘要

摘要: 含裂纹的圆柱体弯曲的研究有十分重要的意义。文献[1]～[4]研究过含径向裂纹或裂纹系的情形,[5]研究过有同心圆弧裂纹的圆柱体的弯曲。本文继续[6]对内部出现在任意位置的直线裂纹的圆柱体在力与裂纹垂直时的弯曲问题,用弹性理论复变函数方法进行了讨论;得到了位移、应力和应力强度因子用级数表示的表达式;对Ah小的这种弯曲问题的应力强度因子给出了好的近似式,分析了它们随裂纹中心的变化规律。最后对裂纹的一个尖端在原点的径向裂纹圆柱体的扭转率和弯曲中心进行了计算,其结果与[1]几乎完全相同。

Abstract: The study of bending of cracked circular cylinders is of more significance.The bending of cylinders containing radical crack or cracks was discussed by refs.[1]-[4] and that of concentrically craked circular cylinders was studied by[5].Continuing[6] and using complex variable methods in elasticity,this paper deals with the bending problems of a circular cylinder,containing an internal linear crack at any position under an acting force perpendicular to the crack.The general forms of displacements,stresses,and stress-intensity factors,expressed in terms of series,are obtained and to this bending problems with small Ah are presented good approximate formulas for the stress-intensity factors whose variations with the center of the crack are analysed.Finally,the twist angle per unit length and the center of bending for the radically cracked circular cylinder,one of whose crack-tips is located at the origin,have been computed and the results are almost the same as that calculated in[1].

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参考文献(8)

[1]	Wigglesworth,L.A.,The flexure and torsion of an internally cracked shaft,Proc.Royal Soc.,(A),170(1939),365-390.
[2]	Wigglesworth,L.A.,Flexure and torsion of a circular shaft with two cracks,Proc.Lon.Mat.Soc.,(A),47(1940),20-37.
[3]	Sih,G.C.,Strength of stress singularities at crack tips for flexural and tosional problems,J.Appl.Mech.,30(1963),419-425.
[4]	汤任草,含径向裂坟系灼圆甘的弯曲和扫洲劣,固沐勺学兴报.3(1983),341-353.
[5]	郭仲衡,有同心圆弧裂缝的圆柱体和圆管的弯曲,力学学报,4(1980),423-427.
[6]	尹昌言,有穿透裂纹的圆柱体弯曲应力及应力强度因子,固体力学学报,4(1983),627-639.
[7]	Мусхелишвили Н.И.,《数学弹性力学的几个基大问题》,科学出版社,(1958).
[8]	尹昌言,有穿透裂纹的圆柱体扭转应力及应力强度因子子,固体力学学报,3(1982),393-405.