Determination of Critical Buckling Loads for Variable Stiffness Euler Columns Using Homotopy Perturbation Method

摘要

In this paper, a new perturbation method namely, Homotopy Perturbation Method (HPM), is applied to buckling of non-uniform columns problem, which is an important engineering problem, because of the fact that determining the buckling loads are important steps in structural analysis and design applications. Columns are primary structural forms and there are numerous studies related to this subject. Application of this new method (HPM) will give researchers a new and powerful tool for solving buckling problems for which finding an exact analytical solution may not be possible. An important point of this technique is, in contrast to traditional perturbation methods, that this new technique does not require a small parameter in an equation to be solved. In this method, according to the homotopy technique, a homotopy with an imbedding parameter p ∈ [0,1] is constructed and imbedding parameter is considered as an expanding parameter. The paper shows the efficiency of the method and accuracy of the obtained analytic approximate solution for the problem.