Nonlinear static and stability analysis of composite beams by the variational asymptotic method

The Variational Asymptotic Method (VAM) that is a powerful method for solving thin-walled beam problems is used for nonlinear static and stability analysis of composite beams. The finite difference and the finite elements methods are used for calculating elastic deformation of beams with clamped-free boundary conditions. The case of simply supported beams is also solved using linear and nonlinear formulations and the results are compared with each other. Next, the shooting method is used for performing nonlinear elasto-static analysis of cantilever beams. Finally by applying perturbations on the equilibrium equations and using an eigenvalue analysis, elastic stability of clamped-free composite beams is analyzed. The obtained results are compared with the available data in the literature that have been obtained using deformation analysis.