Rayleigh-Ritz Solution to Postbuckling Localization of an Axially Loaded Infinite Column on a Foundation

Abstract

Field investigations reveal that railway tracks, pipelines, and pavements are prone to buckling locally as a result of the axial compressive forces caused by thermal loading. These types of structural elements can be simplified as a beam on a nonlinear foundation. A simple and efficient Rayleigh-Ritz method for the postbuckling analysis of an axially loaded column on a nonlinear foundation is proposed herein. The method leads to an integrable formulation of the total potential energy of the column-foundation system and to an expression for the axial shortening in analytical form. The postbuckling deformation consists of an amplitude modulation of the periodic buckle at bifurcation buckling (either symmetric or antisymmetric) in terms of three undetermined coefficients, which can be determined readily. Nonlinear foundation models that include softening and restabilizing behavior are studied, allowing for localization and snaking to be captured in stable and unstable branches of the postbuckling response. The results are shown to agree quite well with numerical studies of the problem.