Variational derivation of equilibrium equations of arbitrarily loaded pre‐stressed shear deformable non‐prismatic composite beams and solution by the DQEM buckling analysis

Abstract

AbstractThe generic equilibrium equations of arbitrarily loaded pre‐stressed non‐prismatic shear deformable composite beams can be derived. The buckling equilibrium equations can be obtained by simplifying the generic equilibrium equations. These equations can be used to develop the differential quadrature element method (DQEM) analysis model of the buckling of shear deformable beams. The DQEM uses the DQ to discretize the buckling equilibrium equation defined on each element, the transition conditions defined on the inter‐element boundary of two adjacent elements and the boundary conditions of the beam. Numerical results of the buckling of shear deformable bar structures solved by the developed numerical algorithm are presented. They prove that the DQEM buckling analysis model is efficient in comparison of convergence rate and numerical stability with the existing numerical techniques such as traditional FDM and some FEM models. Copyright © 2003 John Wiley & Sons, Ltd.