A regular perturbation scheme is here developed for analyzing the dynamic buckling of a lightly damped, imperfect spherical shell struck by an impulse. For simplicity of mathematical analysis, the spherical shell is discretized into time dependent modes and the resultant formulation is that of a two – small parameter problem in which the small parameters serve as agents of asymptotic expansions in a multi-timing perturbation analysis. Unlike most earlier but similar studies, all imperfections and nonlinearities as well as pre-buckling inertia and coupling terms are retained and none is neglected. In the final analysis, the dynamic buckling load is determined and the contributions to buckling of each of the terms are highlighted.
The static buckling load of an imperfect circular cylindrical shell is here determined asymptotically with the assumption that the normal displacement can be expanded in a double Fourier series. The buckling modes considered are the ones that are partly in the shape of imperfection, and partly in the shape of some higher buckling mode. Simply-supported boundary conditions are considered and the maximum displacement and the static buckling load are evaluated nontrivially. The results show, among other things, that generally the static buckling load, S λ decreases with increased imperfection and that the displacement in the shape of imperfection gives rise to the least static buckling load.
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