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.
ReidS. R.ReddyT. Y.Effect of strain hardening on the large plastic deformation of a cantilever. Trans. ASME, J. Appl. Mechanics, 1978, 45, 953–955.
2.
WuX. Q.YuT. X.The complete process of large elastic-plastic deflection of a cantilever. Acta. Mech. Sinica, 1986, 2, 333–347.
3.
LiuJ. H.StrongeW. J.YuT. X.Large deflection of an elastoplastic strain-hardening cantilever. Trans. ASME, J. Appl. Mechanics, 1989, 56, 737–743.
4.
WangB.LuG.YuT. X.A numerical analysis of the large deflection of an elastoplastic cantilever. Struct. Engng and Mechanics, 1995, 3(2), 163–172.
5.
LuanF.YuT. X.An analysis of the large deflection of an elastic-plastic cantilever subjected to an inclined concentrated force. Appl. Math. Mechanics (English edition), 1991, 12, 547–556.
6.
LiuJ. H.AtkinsA. G.PretloveA. J.The effect of inclined loads on the large deflection behaviour of elastoplastic work-hardening straight and pre-bent cantilevers. Proc. Instn Mech. Engrs, Part C: J. Mechanical Engineering Science, 1995, 209(C2), 87–96.
7.
YuT. X.JohnsonW.Influence of axial force on the elastic-plastic bending and springback of a beam. J. Mech. Work. Technol., 1982, 6, 5–21.
8.
HuangX.WangB.LuG.YuT. X.Large deflection of elastoplastic, nonlinear strain-hardening cantilevers. Proc. Instn Mech. Engrs, Part C: J. Mechanical Engineering Science, 2002, 216(C4), 433–446.
9.
LeeK.Large deflections of cantilever beams of non-linear elastic material under a combined loading. Int. J. Non-Linear Mechanics, 2002, 37, 439–443.
10.
LippmannH.Free rigid/plastic plane bending of a slender beam. Ingenieur-Archiv, 1990, 60, 293–302.
11.
ThalmairM.LippmannH.Spatial free plastic forming of slender parts. In Proceedings of IMMM'99, 1999, pp. 161–166.
12.
ThalmairM.LippmannH.Spatial free plastic forming of slender parts—fundamental relations and first example. Int. J. Mech. Sci., 2000, 42, 1851–1865.
13.
ReiglM.LippmannH.MannlV.Air bending as a numerically controlled forming process to produce S-shaped bars. J. Mater. Process. Technol., 1994, 45, 389–394.
14.
HouW. J.YuT. X.SuX. Y.Elastic effect in dynamic response of plastic cantilever beam to impact. Acta Mechanica Solida Sinica, 1995, 16, 13–21.
15.
StrongeW. J.YuT. X.Dynamic Models for Structural Plasticity, 1993 (Springer, London).
16.
TimoshenkoS. P.GereJ. M.Theory of Elastic Stability, 1961 (McGraw-Hill, New York).
