A solution for non-linear buckling problems of the general axisymmetric shell. (Buckling problems of the head of a pressure vessel due to internal pressure and of the U-shaped bellows due to tension)

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A method of solution of the bucking load and the bucking mode of the general axisymmetric shell due to some axisymmetric load considering the non-linear prebuckling deformation is proposed is this study. This problem has been already treated by many general purpose programs using the finite element method or the finite difference method. But it is said that these programs often give somewhat different results from each other for non-linear problems. In this study, a method is proposed to achieve results as accurate as possible. Our method is based on Flugge's shell theory and makes use of the finite difference method. As examples, the partial spherical shell, the tori-spherical head of a pressure vessel and the U-shaped bellows are treated, and some calculated results are compared with those of other researchers.