The Displacement Finite Element Method in Nonlinear Buckling Analysis of Shells

Abstract

The paper compiles the current status of the finite element method in linear and nonlinear buckling analysis of shells. The classical concept via shell theory, the degeneration method, continuum mechanics based and corotationalformulations used in the displacement approach and the corresponding incremental stiffness expression are briefly described. Some comments on the problem of non-uniqueness and stability of the solution and their practical evaluation are given. A classification of displacement dependent pressure loads is presented discussing the symmetry of the problem. The main characteristics of the different classes of shell elements are outlined. Besides flat and curved elements derived from shell theory the survey concentrates on degenerated elements. A detailed review on the main solution strategies in nonlinear shell analyses is presented. Among these are quasi-Newton methods combined with line search and iteration techniques in the displacement and load space. Finally selected numerical examples are described applying isoparametric degenerated elements to bifurcation buckling and nonlinear collapse analyses of shells.