A novel analytical approach for assessing the buckling behavior of non-prismatic elastic columns based on power series

Abstract

The analysis of post-buckling behavior of elastic structures still needs the resolution of a body of non-linear differential equations according to equilibrium equations. Also, the yielding and buckling factors are important in the procedure of designing members under forces such as axial or conjoint axial force and bending moment. In such a way that if the length of the member is too long or the member is thin, before the yielding, buckling will occur in the member, and it is necessary to check and control the member for possible buckling. The present work deals with the stability analysis of elastic columns with variable cross-section under concentrated end load and proposes a simplified approach to the evaluation of the critical buckling force of columns according to the assumptions of the Elastica theory. In this paper, the power series are used to simplify the equations. The numerical issues of the critical buckling force are presented for prismatic and non-prismatic columns subjected to end force, and the effectiveness of this approach is verified for buckling analysis of tapered columns and the rate of accuracy is assessed. The elastic buckling force of elastic structures shows that the introduced model is computationally extremely efficient with the details presented in general. This paper should be a basic reference to compare the results with other researches.