Analytical evaluation of beam deformation problem using approximate methods

Abstract

The beam deformation equation has very wide applications in structural engineering. As a differential equation, it has itsown problem concerning existence, uniqueness and methods of solutions. Often, original forms of governing differentialequations used in engineering problems are simplified, and this process produces noise in the obtained answers.This paper deals with the solution of second order of differential equation governing beam deformation using four analytical approximate methods, namely the Perturbation, Homotopy Perturbation Method (HPM), Homotopy Analysis Method (HAM) and Variational Iteration Method (VIM). The comparisons of the results reveal that these methods are very effective, convenient and quite accurate for systems of non-linear differential equation.

Keywords

• Beam
• differential equation
• Perturbation
• analytical methods
• non-linear