Regular and singular perturbation solutions for bending and torsion of beams

Abstract

For the bending of a beam under axial forces and for the warping of a shaft in torsion, a perturbation solution of the governing differential equation is derived. The beam or shaft may have variable cross sections, variable loading and general end conditions. For both cases—the singular and regular one—the perturbation solutions are explicitly carried out up to (and including) the first perturbation term. For the singular case in addition a solution uniformly valid over the entire beams length is constructed. Two examples illustrating the application are given at the end of this paper.