Buckling of multi-step non-uniform beaks with elastically restrained boundary conditions

摘要

In this paper, eth governing differential equation for buckling of a multi-step non-uniform beam under several concentrated axial forces is established. Te special solutions of bending moment for buckling are found first for eight types of non-uniform beams, then the recurrence formula method and the transfer matrix method for determining the critical buckling force of a multi-step non-uniform beam are proposed. In the recurrence formula method, the two funda- mental solutions of bending moment and the recurrence formulas developed in this paper are used to determine the critical buckling forces for a multi-step non-uniform beam without spring supports, and the four fundamental solutions of displacement and the recurrence formulas are adopted for buckling analysis of such a beam with rotational and translational springs at the ends and intermediate points.