A Boundary Layer Theory for the Buckling of Thin Cylindrical Shells under External Pressure

Shen Hui-shen; Chen Tie-yun

Volume 9 Issue 6

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1988 > 9(6): 515-528

Shen Hui-shen, Chen Tie-yun. A Boundary Layer Theory for the Buckling of Thin Cylindrical Shells under External Pressure[J]. Applied Mathematics and Mechanics, 1988, 9(6): 515-528.

Citation:

Shen Hui-shen, Chen Tie-yun. A Boundary Layer Theory for the Buckling of Thin Cylindrical Shells under External Pressure[J]. Applied Mathematics and Mechanics, 1988, 9(6): 515-528.

Citation:

Shen Hui-shen, Chen Tie-yun. A Boundary Layer Theory for the Buckling of Thin Cylindrical Shells under External Pressure[J]. Applied Mathematics and Mechanics, 1988, 9(6): 515-528.

PDF( 771 KB)

A Boundary Layer Theory for the Buckling of Thin Cylindrical Shells under External Pressure

Shanghai Jiaotong University, Shanghai

Received Date: 1985-09-30
Publish Date: 1988-06-15

Abstract

Abstract

Based on the boundary layer theory for the buckling of thin elastic shells-suggested in ref. [14], the buckling and postbuckling behavior of clamped circular cylindrical shells under lateral or hydrostatic pressure is studied applying singular perturbation method by taking deflection as perturbation parameter. The effects of initial geometric imperfection are also considered. Some numerical results for perfect and imperfect cylindrical shells are given. The analytical results obtained are compared with some experimental data in detail, which shows that both are rather coincident.

FullText(HTML)

References(22)

References

[1]	Amazigo,J.C.,Asymptotic analysis of the buckling of externally pressurized cylinders with random imperfections,Quar.Appl.Math.,31(1974),429-442.
[2]	Amazigo,J.C.and W.B.Fraser,Buckling under external pressure of cylindrical shells with dimple shaped initial imperfections,Int.J.Solids Structures,7(1971),883-900.
[3]	Batdorf,S.B.,A simplified method of elastic-stability analysis for thin cylindrical shells,NACA Report,No.874(1947).
[4]	Batista,R.C.and J.G.A.Croll,Simple buckling theory for pressurized cylinders,Proc.ASCE,108,EM5(1982),927-944.
[5]	Bijlaard,P.P.,Buckling stress of thin cylindrical clamped shells subject to hydrostatic pressure,J.Aero.Sci.,21(1954),852-853.
[6]	Budiansky,B.and J.C.Amazigo,Initial post-buckling behavior of cylindrical shells under external pressure,J.Math.Phys.,47,3(1968),223-235.
[7]	Donnell,L.H.,Effect of imperfections on buckling of thin cylinders under external pressure,J.Appl.Mech.,23(1956),569-575.
[8]	Donnell,L.H.,Effect of imperfections on buckling of thin cylinders with fixed edges under external pressure,Proc.3rd U.S.Nat.Conger.Appl.Mech.(1958),305-311.
[9]	Kempner,J.,K.A.V.Pandalai,S.A.Patel and J.Crouzet-Pascal,Postbuckling behavior of circular cylindrical shells under hydrostatic pressure,J.Aero.Sci.,24(1957),253-264.
[10]	Kirstein,A.F.and E.Wenk,Jr.,Observations of snap-through action in thin cylindrical shells under external pressure,Proc.SESA,14,1(1956),205-214.
[11]	von Mises,R.,Der Kritische Aussendruck zylindrischer Rohre,Zeit.V.D.I.,58(1914),750-755.
[12]	von Mises,R.,Der Kritische Aussendruck fr allseits belastete zylindrische Rohre,Fest.zum 70 Geburstag yon Prof.Dr.A.Stodola,Zurich(1929),418-430.
[13]	Nash,W.A.,Buckling of thin cylindrical shells subject to hydrostatic pressure,J.Aero.Sci.,21(1954),354-355.
[14]	Shen,H.S.and T.Y.Chen,A boundary layer theory for the buckling of thin cylindrical shells under axial compression,The Advances of Applied Mathematics and Mechanics in China,(1988).
[15]	Sturm,R.G.,A study of the collapsing pressure of thin-walled cylinders,Eng.Exp.Sta.Bull.,Univ.Illinois,329(1941).
[16]	Tennyson,R.C.,The effect of shape imperfections and stiffening on the buckling of circular cylinders,Buckling of Structures,ed.by B.Budiansky,IUTAM Syrup.(1974),251-273,Springer-Verlag,Berlin Heidelberg,New York(1976).
[17]	Weingarten,V.I.and P.Seide,Elastic stability of thin-walled cylindrical and conical shells under combined external pressure and axial compression,AIAA J.,3,5(1965),913-920.
[18]	Windenburg,D.F.and C.Trilling,Collapse by instability of thin cylindrical shells under external pressure,Trans.ASME,56(1934),819-825.
[19]	Yamaki,N.,Influence of prebuckling deformations on the buckling of circular cylindrical shells under external pressure,AIAA J.,7,4(1969),753-755.
[20]	Yamaki,N.and K.Otomo,Experiments on the postbuckling behavior of circular cylindrical shells under hydrostatic pressure,Exp.Mech.,13,7(1973),299-304.
[21]	Yamaki,N.and J.Tani,Postbuckling behavior of circular cylindrical shells under hydrostatic pressure,ZAMM,54,11(1974),709-714.
[22]	Yamaki,N.,Elastic Stability of Circular Cylindrical Shells,Elsevier Science Publishers,B.V.(1984).

Relative Articles

[1]	LI Chen, TIAN Xue-kun, WANG Hai-ren, MIAO Ya-nan. Thermal Buckling of Thin Spherical Shells Under Interaction of Uniform External Pressure and Uniform Temperature[J]. Applied Mathematics and Mechanics, 2015, 36(9): 924-935. doi: 10.3879/j.issn.1000-0887.2015.09.004
[2]	MA Jian-qing, XU Xin-sheng. Dynamic Buckling of Cylindrical Shells Under Coupled Impact Loads[J]. Applied Mathematics and Mechanics, 2014, 35(5): 510-522. doi: 10.3879/j.issn.1000-0887.2014.05.005
[3]	ZHONG Wei-zhou, SONG Shun-cheng, CHEN Gang, HUANG Xi-cheng, HUANG Peng. Stress Field of Orthotropic Cylinder Subjected to Axial Compression[J]. Applied Mathematics and Mechanics, 2010, 31(3): 285-294. doi: 10.3879/j.issn.1000-0887.2010.03.004
[4]	ZHOU Jia-xi, DENG Zi-chen, HOU Xiu-hui. On the Critical Velocity of the Sandwich Cylindrical Shell to Moving Internal Pressure[J]. Applied Mathematics and Mechanics, 2008, 29(12): 1426-1434.
[5]	NING Jian-guo, SONG Wei-dong. Perforation of Plastic Spherical Shells Under Impact by Cylindrical Projectiles[J]. Applied Mathematics and Mechanics, 2006, 27(2): 211-216.
[6]	SHEN Hui-shen. Postbuckling of Pressure-Loaded Shear Deformable Laminated Cylindrical Panels[J]. Applied Mathematics and Mechanics, 2003, 24(4): 357-366.
[7]	CHENG Chang-jun, ZHANG Neng-hui. Dynamical Behavior of Viscoelastic Cylindrical Shells Under Axial Pressures[J]. Applied Mathematics and Mechanics, 2001, 22(1): 1-8.
[8]	SHEN Hui-shen. Buckling and Postbuckling of Laminated Thin Cylindrical Shells under Hygrothermal Environments[J]. Applied Mathematics and Mechanics, 2001, 22(3): 228-238.
[9]	Shen Huishen. Postbuckling of Imperfect Stiffened Cylindrical Shells under Combined External Pressure and Heating[J]. Applied Mathematics and Mechanics, 1998, 19(5): 385-398.
[10]	Sun Haihong, Chen Tieyun. Koiter-Boundary Layer Singular Perturbtion Method forAxial Compressed Stiffened Cylindrical Shells[J]. Applied Mathematics and Mechanics, 1997, 18(5): 459-467.
[11]	Han Qiang, Ma Hongwei, Zhang Shanyuan, Yang Guitong, Wu Jike. The Dynamic Buckling Problem Caused by Propagation of Stress Wave in Elastic Cylindrical Shells under impact Torque[J]. Applied Mathematics and Mechanics, 1996, 17(1): 1-7.
[12]	Huang Chengyi, Liu Tuguang, Zheng Jijia. Elastic Pulse Buckling of Cylindrical Shells under Radial Impulsive Loading[J]. Applied Mathematics and Mechanics, 1996, 17(8): 735-741.
[13]	Chang Ming, Chang Li-li. Analysis of the Eccentric Cylindrical Thin Shell[J]. Applied Mathematics and Mechanics, 1994, 15(9): 841-848.
[14]	Zhao Xing-hua. Stress-Anlysis of Thick Ring Shell Sumitted to the Action of Internal Pressure[J]. Applied Mathematics and Mechanics, 1994, 15(12): 1047-1055.
[15]	Mu Jian-chun, Wu Wen-zhou, Yang Gui-tong. A Numerical Calculation of Dynamic Buckling of a Thin Shallow Spherical Shell under Impact[J]. Applied Mathematics and Mechanics, 1992, 13(2): 111-119.
[16]	Shen Hui-shen, Zhou Pin, Chen Tie-yun. Buckling and Postbuckling of Stiffened Cylindrical Shells under Axial Compression[J]. Applied Mathematics and Mechanics, 1991, 12(12): 1127-1139.
[17]	Sun Ren-bo, Wang Dai-yu, Zou Ding-qi. Calculation for Cylindrical Shell under Local Vertical Loadings[J]. Applied Mathematics and Mechanics, 1990, 11(2): 179-188.
[18]	He Fu-bao, Yu Zhi-meng. The Initial Post-Buckling Behavior of Ring Stiffened Shells under Hydrostatic Pressure[J]. Applied Mathematics and Mechanics, 1988, 9(11): 951-962.
[19]	Wang Dai-yu, Chen Shan-lin, Wu Guo-ping. The Ring Shells under Gravitative Loads[J]. Applied Mathematics and Mechanics, 1986, 7(7): 637-646.
[20]	Wu Shen-rong. Studies of Nonlinear Theories for Thin Shells[J]. Applied Mathematics and Mechanics, 1983, 4(2): 221-231.