A new approach for elasto-plastic finite strain analysis of cantilever beams subjected to uniform bending moment

The reliability and limits of solutions for static structural analysis depend on the accuracy of the curvature and deflection calculations. Even if the material model is close to the actual material behavior, physically unrealistic deflections or divergence problems are unavoidable in the analysis if an appropriate fundamental kinematic theory is not chosen. Moreover, accurate deflection calculation plays an important role in ultimate strength analysis where in-plane stresses are considered. Therefore, a more powerful method is needed to achieve reliable deflection calculation and modeling. For this purpose, a new advanced step was developed by coupling the elasto-plastic material behavior with precise general planar kinematic analysis. The deflection is generated precisely without making geometric assumptions or using differential equations of the deflection curve. An analytical finite strain solution was derived for an elasto-plastic prismatic/non-prismatic rectangular cross-sectioned beam under a uniform moment distribution. A comparison of the analytical results with those from the Abaqus FEM software package reveals a coherent correlation.