Large deflection response of an elastic, perfectly plastic cantilever beam subjected to a step loading

This paper studies the large deflection response of an elastic, perfectly plastic cantilever beam subjected to a step load using finite difference method. A computational stability requirement is proposed to determine the relationship between the time-step and the element size. It is demonstrated that the numerical solution is convergent if the stability requirement can be satisfied. The deformation mechanism of the cantilever beam is studied based on the instantaneous distributions of bending moment and curvature during the response of the beam. It is found that the deformation mechanism depends on the magnitude of the step load. When the step load is moderate, only a single stationary plastic bending hinge is formed at the root of cantilever beam during the response. For intensive loading magnitude, stationary plastic bending hinges at both interior and root positions are formed with the latter as the predominant deformation mode during the response of the cantilever beam, which is supported by the rigid, perfectly plastic analysis. The limitations of the classical rigid, perfectly plastic cantilever beam model are discussed.