Buckling of shells: non-classical analysis

Abstract

Introduction The ‘classical’ analysis of the buckling of thin elastic cylindrical shells was presented in the preceding chapter. There it was pointed out that in some circumstances the results of the classical analysis are reliable, and can form the basis of rational design procedures; but also that there are other circumstances in which the results of the classical analysis can be grossly unsafe. The task of the present chapter is to consider this second class of problem. It was pointed out in sections 14.1 and 14.2.3 that the key to the situation is the use of nonlinear theories of elastic buckling. This is a very large subject indeed, which has attracted much attention from many workers since the early days of the use of thin-sheet metal for the construction of aircraft. The aim of this chapter is to investigate the particular problem of a thin-walled cylindrical shell under axial compression, and to attempt to describe, by the means at our disposal, some important features of the behaviour. In chapter 16 we shall tackle a different problem which also demands nonlinear analysis; and indeed we shall find some common aspects with chapter 15. At the end of the two chapters the reader should be in a position to appreciate the literature of the field (e.g. Hutchinson & Koiter, 1970; Brush & Almroth, 1975; Bushnell, 1981): this covers not only the general theory of elastic post-buckling behaviour, but also specific applications to cylindrical and non-cylindrical shells and panels, with and without reinforcing ribs, etc.