NONLINEAR THIN SHELL THEORIES FOR NUMERICAL BUCKLING PREDICTIONS

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 s hells. Most of these theories were developed in the pre-computer era f or analytical studies when simplicity was emphasized and terms judged to be small relative to other terms were omitted. With the availabilit y of greatly increased computing power in recent years, accuracy rathe r than simplicity is given more emphasis. Additional complexity in the strain-displacement relations leads to only a small increase in compu tational 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 no nlinear and buckling analysis. This paper first describes a set of non linear strain-displace ment relations for thin shells of general form developed directly from the nonlinear theory of three-dimensional soli ds. In this new theory, all nonlinear terms, large and small, are reta ined. When specialized for thin shells of revolution, this theory redu ces to that previously derived by Rotter and Jumikis and others. Analy tical and numerical comparisons are carried out for thin shells of rev olution between Rotter and Jumikis' theory as a special case of the pr esent theory and other commonly used nonlinear theories. The paper con cludes with comments on the suitability of the various nonlinear shell theories discussed here for use in numerical buckling analysis of com plex branched shells. (C) 1998 Elsevier Science Ltd. All rights reserv ed.