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The subject of buckling and post-buckling has a relatively short history for composite laminated
shells in comparison with isotropic homogenous shells. Nevertheless, during this short time
considerable research has taken place and a remarkable attention has been became to the stability
of anisotropic shell. Numerous studies on the modeling and analysis of composite laminated
cylindrical shells have been performed. However, the theories used in these analyses are mostly
extensions of the various isotropic shell models. Recently, for the purpose of optimum design of
composite laminated shell structures, fully anisotropic laminated cylindrical shells attracted more
attention by Weaver, Wong and Weaver, Semenyuk and Trach and Takano. In composite
laminated cylindrical shells, when the angles of fibers are not parallel in the cylindrical axis or not
in the circumferential plane, the bending-twist and twist-extension couplings are presented.
Hilburger et al. developed an analytical solution to predict buckling load of the composite cylinder
with cutout. Smerdov (2000) presented a computational method in optimal formulation of
optimization problems on laminated cylindrical shells under compressive axial loads. It is shown
that, for most practical cases, there is no gain in increasing the number of the layers above four and
the number of variable parameters above two. Weaver et al. (2002b) pointed out that, even for a
quasi-isotropic laminated cylindrical shell consisting of 0, 90, +45/−45 plies, the minimum number
of layers is 48 when extension-twist and flexural-twist couplings are vanished.