Exact semi-inverse solutions for the elastoplastic deformation of beam with power law material model

Engineering analyses of beams are based on the proper guesstimate of deformation fields. Up until now, the analyses of beams are widely proposed and experienced in elastic region of materials behavior. This paper considers the elastoplastic engineering analysis of beams. In this regard, following the definition of a proper deformation pattern known as classical Euler- Bernoulli model and using the variational calculus principals the governing equations are extracted. In this analysis the behavior of material obeys the Romberg-Osgood model and yielding is based on the von Mises criterion. Different numerical solutions are represented for the solution of these complicated equations in the literature. In this paper the exact solution is provided for a thin beam under the action of uniformly distributed load by using the two analytical methods of homotopy and Adomian for the clamped- clamped boundary conditions. In verification phase, the deformation of beam is compared with the results of Abaqus software. Different graphical representations are provided for the results of the analytical solutions and simulations. Using these data, the level of consistency between the simulated solutions in one side and the Adomian and homotopy techniques on the other side, are assessed. At the end, the validity of applying the classical engineering theory of beams in the elastoplastic analyses is discussed.