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.

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

• Publish Date: 1988-06-15
• 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.
•  [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).

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