Yin Chang-yan, Zu Cheng-de. Bending of a Circular Cylinder Containing a Crack[J]. Applied Mathematics and Mechanics, 1987, 8(11): 1015-1026.
 Citation: Yin Chang-yan, Zu Cheng-de. Bending of a Circular Cylinder Containing a Crack[J]. Applied Mathematics and Mechanics, 1987, 8(11): 1015-1026.

# Bending of a Circular Cylinder Containing a Crack

• Publish Date: 1987-11-15
• 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].
•  [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.

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