Large deflection of elastoplastic beams with prescribed moving and rotating ends

The large deflection of an elastoplastic beam with prescribed moving and rotating end conditions is investigated to simulate its air-bending process. A finite difference model is developed and governing equations in terms of rotations of elements were derived. Due to both geometrical and material non-linearities, only numerical solutions are obtained by using an iteration procedure. Four typical examples with various moving/rotating boundary conditions are shown by graphs. Numerical analyses also show the evolution of the plastic region and the effects of springback and loading path on the deformed profiles.