Research of Elastic and Elastic-Plastic Deformation on Bending Problems of Variable Stiffness Beams

A novel variable stiffness model was proposed for analyzing elastic-plastic bending problems with arbitrary variable stiffness in detail. First, it was assumed that the material of a rectangular beam is an ideal isotropic elastic-plastic material, whose elastic modulus, yield strength, and section height are functions of the axial coordinates of the beam respectively. Considering the effect of shear on the deformation of the beam, the elastic and elastic-plastic bending problems of the axially variable stiffness beam were studied. Then, the analytical solutions of the elastic and elastic-plastic deformation of the beam were derived when the cross-section height and the elastic modulus of the material were varied by special function along the length of the beam respectively. The elastic and elastic-plastic analysis of the variable stiffness beam was carried out using Differential Quadrature Method (DQM) when the bending stiffness varied arbitrarily. The influence of the axial variation of the bending stiffness on the elastic and elastic-plastic deformation of the beam was analyzed by numerical simulation, DQM, and finite element method (FEM). Simulation results verified the practicability of the proposed mechanical model, and the comparison between the results of the solutions of DQM and FEM showed that DQM is accurate and effective in elastic and elastic-plastic analysis of variable stiffness beams.