Eigenvalue branching configurations and the Rayleigh-Ritz procedure

Abstract

A general theory of elastic post-buckling, applicable to a wide class of structural eigenvalue problems, is developed in generalized coordinates. Attention is restricted to the initial post-buckling path of the structural system on a plot of the load against the critical principal coordinate, and exact first-order solutions for the path are presented. These solutions are compared with the predictions of the non-linear Rayleigh-Ritz analysis in which the linear buckling mode is employed as the assumed form, and theorems concerning the results of this analysis are established.