Exact stress and deformation analysis in elastoplastic Ramberg-Osgood beam

Elastoplastic deformation and stress distributions in a thin or classical Euler-Bernoulli beam are derived by an exact solution methodology. In the formulations phase, the Hencky deformation theory of plasticity is employed. It is assumed that material of Ramberg-Osgood behavior yields according to von Mises criterion. Using the principals of variational calculus and assuming a tri-axial field of stress, governing equations of elastoplastic beam are extracted. Exact solution of resulting nonlinear integro-differential equations are obtained by using the analytical methods of homotopy and Adomian. In the exemplary study of clamped-clamped beam, the fields of deformation are compared with the results of ABAQUS software. Different graphical representations are provided to show the results of analytical solutions and computer simulations. The level of consistency between the computer simulations and solutions of Adomian and homotopy techniques is assessed. At the end, the capability of classical engineering beam theory for the elastoplastic analysis is assessed.