14 - Buckling of shells: classical analysis

Summary

Buckling of structures

Buckling is a word which is used to describe a wide range of phenomena in which structures under load cease to act in the primary fashion intended by their designers, but undergo instead an overall change in configuration. Thus a rod which was originally straight, but has bowed laterally under an end-to-end compressive load has buckled; and so has a cylindrical shell, which has crumpled up under the action of the loads applied to it.

The buckling of structures is an important branch of structural mechanics, because buckling often (but not always) leads to failure of structures. It is particularly important in shell structures because it often occurs without any obvious warning, and can have catastrophic effects.

The buckling of shells has been studied intensively for about four decades, and the information now available on the subject is enormous. The aim of this chapter and the two following is to give an introduction to the subject in the simplest possible terms.

The ‘classical’ theory to be described in this chapter is merely an extension into the field of shell structures of what is often described as the ‘Euler’ theory of buckling of simple struts which are initially straight. For some problems in shell buckling this kind of theory is adequate, and well attested by experiment; but for other problems it is inadequate and indeed can be positively misleading.