Springback Variation Principles in Materials Forming Processes

Abstract:

The conceptions of springback anti-couple systems and equations are initially given. By the use of the weighted residual method to the springback anti-couple equations, the springback principles of minimum potential energy and minimum complementary energy are established. Meanwhile, the springback principle of minimum potential energy is applied to calculating springback deformations of a curved beam under the radial and circumferential forces and end bending moments.

• Periodical: Applied Mechanics and Materials (Volumes 29-32)
• Pages: 525-530
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.29-32.525
• Online since: August 2010
• Authors: Bao Lian Fu, Ying Jie Chen
• Keywords: Materials Forming Process, Springback, Springback Anti-Couple Equation, Springback Variational Principle

References

[1] Brunet, M. A., 1987, A finite analysis of springback in plan folding with binders of high strength steel sheets, Computational Methods for Predicting Material Processing Defects, M. Predelranu (eds), Elsevier Science Publishers B. V. Amsterdam, pp.47-56.

DOI: 10.1016/b978-0-444-42859-2.50011-9

[2] Chien W. Z., 1980, Variational methods and finite methods. Vol. 1 Science Press (1980) (in Chinese).

[3] Fu B. L., 1994, The variational principles of coupled systems in photoelasticity, Applied Mathematics and Mechanics, 15 (1), pp.37-48.

[4] Fu B. L., 1996, Coupled variational principles and generalized coupled variational principles in photoelasticity, Applied Mathematics and Mechanics, 17 (1), pp.39-44.

DOI: 10.1007/bf00131293

[5] Fu B. L., 1999, Simulated variational principles and generalized simulated variational principles for similarly non-coupled systems in metal forming technology, Engineering Mechanics, 16 (2), pp.52-59. (in Chinese).

[6] Gardiner F. J., 1957, The springback of metals, Trans. ASME, 79, pp.1-9.

[7] Hu X. C., 1981, Varitional principles and their applications in elasticity, Science Press (in Chinese)Huang, M., Gerdeem J. C., 1994 Springback of doubly curved developable sheet metal surface, 22 An overview, SAE Trans. , Section 5, 940938, pp.718-731.

DOI: 10.4271/940938

[8] Johnson, W. and Yu, T. X., 1981, On springback after the pure bending of beams and plates of elastic work-hardening material--Ⅲ, Int. J. Mech. Sci, 23, pp.687-696.

DOI: 10.1016/0020-7403(81)90022-9

[9] Washizy, .K. , 1975, Varitional methods in elasticity and plasticity, Pergamon Press. Reissner, E. , 1950, On a variational theorem in elasticity, Journal of Mathematics and Physics, 29 (2) , pp.90-95.

DOI: 10.1002/sapm195029190

[10] Timoshenko, S. P. and Goodier, J. N., 1970, Theory of elasticity (Third Edition), MeGraw-Hill Book Company.

[11] Wu L. W., 1993, Springback and residual stress analysis for sheet metal forming processes by dynamic relaxation in conjunction with finite element method, ICTP'93, pp.1840-1845.

[12] Yu, Y., Zhang L. C. and Yu T. X., 1989, The elastic-plastic pure bending and springback of L-shaperd beams, Int. J. Mech. Sci , 29, pp.425-433.