Post-buckling analysis of a simply supported beam under uniform thermal loading

Abstract

This paper focuses on post-buckling analysis of a simply supported beam subjected to a uniform thermal loading. The material of the beam was assumed as isotropic and hyper elastic. Both ends of the beam were supported by pins (pinned-pinned beam). In this study, finite element model of the beam was constructed by using total Lagrangian finite element model of two dimensional continuums for an eight-node quadratic element. The considered highly non-linear problem was solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. Based on the above mentioned solution procedure, analysis of large thermal bending and buckling/post buckling responses of the beam subjected transversally uniform temperature rise and with immovably pinned-pinned ends were presented. Characteristic curves showing the relationships between the beam displacements and temperature rise were illustrated. The results are compared with the published results obtained by using Timoshenko beam theory. Numerical results showed that the results of two dimensional continuum model and those of Timoshenko beam theory differ from each other with decrease of the slenderness of the beam. Therefore it is necessary to use a finite element model of two dimensional continuums in modelling the beam in the case of small slenderness. Key words: Post-buckling analysis, total Lagrangian finite element model, two dimensional solid continuum, uniform temperature rise.