Some closed-form solutions for buckling of straight beams with varying cross-section by Variational Iteration Method with Generalized Lagrange Multipliers

Abstract

This study aims to derive approximate closed-form solutions for critical loads of straight beams with variable cross-section. The governing equations are derived for purely flexible beam for small displacements and rotation and turned into non-dimensional form. Approximate solutions to the set of equations for stability problems are searched by Variational Iteration Method with Generalized Lagrange Multipliers. It turns out that highly accurate approximate buckling loads of cantilever beams with variable section can be obtained in closed-form. Many novel closed-form solutions for critical load of such structures, which may serve as benchmark solutions, are presented.