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From Lecture 8.7, "Basic Analysis of Shell Structures",
ESDEP WG 8, "Plates and Shells"
Website:
http://www.fgg.uni-lj.si/kmk/esdep/master/wg08/l0700.htm
If a very thin, unstiffened, isotropic, axially compressed cylindrical shell is loaded far into its post-buckled state, the pattern of deformation resembles the Yoshimura pattern shown here. (See the previous slide and the next 6 slides.) The Yoshimura pattern forms a developable surface, that is, a surface for which there is little or no membrane strain energy. The prebuckling membrane energy is partly converted into bending energy which is concentrated along the lines of intersection of the little flat triangular areas of the Yoshimura pattern. The Yoshimura pattern corresponds to the minimum post-buckling axial load that can be supported by the buckled cylindrical shell.
See:
Yoshimura, Y., “On The Mechanism Of Buckling Of A Circular Cylindrical Shell Under Axial Compression”, NACA-TM-1390, 1 January, 1951, OSTI Identifier OSTI ID: 4373171
ABSTRACT: The present paper deals with the buckling of a circular cylindrical shell under axial compression from the viewpoint of energy and the characteristics of deformation. It is shown first, both theoretically and experimentally, that the reason why the buckling of a cylindrical shell is quite different from that of a flat plate is attributable to the existence of a nearly developable surface far apart from the original cylindrical surface. Based upon this result, the experimental fact that the buckling is really not general but local, that is, that the buckled region is limited axially to a range of 1.5 times the wave length of the lobe, is explained by the theoretical result that the minimum buckling load is smaller in the local buckling than in the general buckling case. The occurrence of local buckling is affirmed also from the viewpoint of the energy barrier to be jumped over during buckling, and from a comparison of the theoretical post-buckling state with the experimental results. Finally, the local buckling with the load applied by a spring is analyzed, and it is proved that the minimum buckling load increased with an increase of rigidity of the spring.
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