Keywords: elastic buckling, cylindrical shell, cylindrical panel, plates, lower bound.

This paper is devoted to a cylindrical panel and cylindrical shell subjected to axial compression. Stability equations of these shells with geometric imperfections were solved analytically. Equilibrium paths marked as classical upper and lower critical stresses have also been determined. Next, nonlinear equations of a rectangular plate subjected to longitudinal compression were solved and equilibrium paths were established. Comparison of the equilibrium paths to geometric imperfection of the cylindrical panel and rectangular plate allowed the lower critical stress of the cylindrical panel and of cylindrical shell, to be determined. The classical upper critical stress of axially compressed cylindrical shell ( Lorenz-Timoshenko-Southwell stress) is of the following form:

while the classical lower critical stress (from the nonlinear von Kármán-Donnell equations) is:

Experimental studies of these shells show that experimental values of critical stresses are lower than the corresponding theoretical values. In practical calculations, a "knockdown" factor has been introduced.

Solution of nonlinear von Kármán-Donnell equations, with geometrical imperfections, allows equilibrium path of the compressed rectangular plate and of cylindrical panel, to be determined.

Existence of geometrical imperfection in the plate does not affect its critical stress. On the other hand, critical stresses of the cylindrical panel, or shell, strongly depend on geometrical imperfections. The equilibrium path of the imperfect plate is a curve with no extreme points, while for the imperfect cylindrical panel or shell it has maximum and minimum. In a particular imperfection case of this curve only an inflection point may occur.

On the grounds of an analytical solution the lower critical stress of the cylindrical panel may be assumed in the following form

The critical stress for the rectangular plate is:

where is the length of a circumferential half-wave of a buckling shell.

The critical stress of the cylindrical panel or the cylindrical shell becomes:

The value of the stress is equal to the lower limit of experimental critical stresses for cylindrical panels and cylindrical shells [1]. The problems of stability of cylindrical shells [2,3,4,5] are subject to-day to theoretical and experimental studies.

1

L.H. Donnell, "Beams, plates and shells", McGraw-Hill Book Comp., 1976.

2

D.Al. Galib, A. Limam, "Experimental and numerical investigation of static and dynamic axial crushing of circular aluminum tubes", Thin-Walled Structures, 42, 1103-1137, 2004. doi:10.1016/j.tws.2004.03.001

3

G.D. Galletly, J. Blachut, "Axially-compressed cylindrical shells - a comparison of experiment and theory", Inelastic Solids and Structures, M. Kleiber and J.A. König (Ed.), Pineridge Press Limited, 257-276, 1990.

4

A. Khamlichi, M. Bezzazi, A. Limam, "Buckling of elastic cylindrical shells considering the effect of localized axisymmetric imperfections", Thin-Walled Structures, 42, 1035-1047, 2004. doi:10.1016/j.tws.2004.03.008

5

J.G. Teng, J.M. Rotter (Ed.), "Buckling of thin metal shells", Spon Press: London, New York, 2004.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £135 +P&P)