Recursive Differentiation Method for Boundary Value Problems: Application to Analysis of a Beam-Column on an Elastic Foundation

Abstract

Abstract In the present work, the recursive differentiation method (RDM) is introduced and implemented to obtain analytical solutions for differential equations governing different types of boundary value prob- lems (BVP). Then, the method is applied to investigate the static behaviour of a beam-column resting on a two parameter foundation subjected to different types of lateral loading. The analytical solutions obtained using RDM and Adomian decomposition method (ADM) are found similar but the RDM requires less mathematical effort. It is indicated that the RDM is reliable, straightforward and efficient for investigation of BVP in finite domains. Several examples are solved to describe the method and the obtained results reveal that the method is convenient for solving linear, nonlinear and higher order ordinary differential equations. However, it is indicated that, in the case of beam-columns resting on foundations, the beam-column may be buckled in a higher mode rather than a lower one, then the critical load in that case is that accompanies the higher mode. This result is very important to avoid static instability as it is widely common that the buckling load of the first buckling mode is always the smaller one, which is true only in the case of the beam-columns without foundations.