Post-buckling analysis of variable cross-section cantilever beams under combined load via differential quadrature method

Abstract

Based on the geometrically nonlinear theory of extensible elastic rods, the governing equations for post-buckling of variable crosssection cantilever beams subjected to a concentrated axial load at its free end and a non-uniformly distributed axial load are formulated. The Differential Quadrature Method (DQM) as a simple and computationally efficient numerical method is used to obtain the critical buckling load. The accuracy of the method is verified by comparing the results with those of the analytical result from the elliptical integral, and other methods such as shooting method or multiple scale method. The post buckling configuration of the beam is obtained for different loading conditions.

Failure Modes of Serially Isolated System under Large Deformation

“…Henceforth, the buckling loads will depend on the applied boundary conditions and continuity conditions. Finally, the DQ discretized form of the resulting equations can be expressed as [12][13][14][15]:…”