Nonlinear thin shell theories for numerical buckling predictions

Abstract

A basic building block in any numerical (geometrically) nonlinear and buckling analysis is a set of nonlinear strain–displacement relations. A number of such relations have been developed in the past for thin shells. Most of these theories were developed in the pre-computer era for analytical studies when simplicity was emphasized and terms judged to be small relative to other terms were omitted. With the availability of greatly increased computing power in recent years, accuracy rather than simplicity is given more emphasis. Additional complexity in the strain–displacement relations leads to only a small increase in computational effort, but the omission of a term which may be important in only a few complex problems is a major flaw. It is therefore necessary to re-examine classical shell theories in the context of numerical nonlinear and buckling analysis. This paper first describes a set of nonlinear strain–displacement relations for thin shells of general form developed directly from the nonlinear theory of three-dimensional solids. In this new theory, all nonlinear terms, large and small, are retained. When specialized for thin shells of revolution, this theory reduces to that previously derived by Rotter and Jumikis and others. Analytical and numerical comparisons are carried out for thin shells of revolution between Rotter and Jumikis' theory as a special case of the present theory and other commonly used nonlinear theories. The paper concludes with comments on the suitability of the various nonlinear shell theories discussed here for use in numerical buckling analysis of complex branched shells.