ELASTIC POSTBUCKLING ANALYSIS VIA FINITE-ELEMENT AND PERTURBATION TECHNIQUES .1. FORMULATION

The main equations for the equilibrium, stability and critical state analysis of discrete elastic systems are presented following the works of Thompson, but in such a way that the original set of generalized coordinates and loads are preserved in the Total Potential Energy. This introduces differences in the resulting equations in bifurcation analysis but does not introduce any new feature regarding the physics of the problem. The new formulation is approximated by means of a standard finite element approach based on interpolation of displacements, in which the derivatives of the potential energy are approximated. The terms retained are those of moderately large rotation theory. The energy analysis is finally related to the more conventional finite element notation in terms of stiffness matrices, and it is shown how in such a way it can be included in present day codes. Part 2 of the paper deals with applications to the analysis of shells of revolution using a semi-analytical approximation. Two cases are presented in detail: bifurcation in axisymmetric and in asymmetric modes, and the results show good correlation with those of other authors. The influence of load and geometric imperfections is evaluated.