The Shaping of a Triangle Steel Plate into an Equilateral Vertical Steel by Finite-Element Modeling
Authors: Tsung-Chia Chen
The orthogonal processes to shape the triangle steel plate into a equilateral vertical steel are examined by an incremental elasto-plastic finite-element method based on an updated Lagrangian formulation. The highly non-linear problems due to the geometric changes, the inelastic constitutive behavior and the boundary conditions varied with deformation are taken into account in an incremental manner. On the contact boundary, a modified Coulomb friction mode is specially considered. A weighting factor r-minimum is employed to limit the step size of loading increment to linear relation. In particular, selective reduced integration was adopted to formulate the stiffness matrix. The simulated geometries of verticality could clearly demonstrate the vertical processes until unloading. A series of experiments and simulations were performed to validate the formulation in the theory, leading to the development of the computer codes. The whole deformation history and the distribution of stress, strain and thickness during the forming process were obtained by carefully considering the moving boundary condition in the finite-element method. Therefore, this modeling can be used for judging whether a equilateral vertical steel can be shaped successfully. The present work may be expected to improve the understanding of the formation of the equilateral vertical steel.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1085808Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1098
 D.S. Malkus and T.J.R. Hughes, "Mixed finite-element methods-reduced and selective integration techniques: a unification of concepts," Comput. Meth. Appl. Mech. Eng., vol. 15(1), 1978, pp.63-81.
 R.M. McMeeking and J.R. Rice, "Finite element formulations for problems of large elastic-plastic deformation," Int. J. Solids Structures, vol. 11, 1975, pp.601-606.
 H.L. Cao and C. Teodosiu, "Finite element calculation of springback effects and residual stress after 2D deep drawing," Conference proceedings: Computational Plasticity - fundamentals and applications, Barcelona, Spain, 18-22 September 1989, pp.959-971.
 Y. Yamada, N. Yoshimura and T. Sakurai, "Plastic stress-strain matrix and its application for the solution of elastic-plastic problems by the finite element method," Int. J. of Mech. Sci., vol. 10, 1968, pp.343-354.
 E. Hinton and D.R. Owen, Finite Element Software for Plates and Shell. Pineridge, Swansea, UK, 1984.
 T.J.R. Hughes, The Finite Element Method. Prentice-Hall, Englewood Cliffs, NJ, 1987.
 T.J.R. Hughes, "Generalization of selective integration procedures to anisotropic and nonlinear media," International Journal of Numerical Methods in Engineering, vol. 15, 1980, pp.1413-1418.
 H.B. Shim and D.Y. Yang, "Elastic-plastic finite element analysis of deep drawing processes by membrane and shell elements," Journal of Manufacturing Science and Engineering, Transactions of the ASME, vol. 119, 1997, pp.341-349.
 D.K. Leu, T.C. Chen, Y.M. Huang, "Influence of punch shapes on the collar-drawing process of sheet steel," Journal of Materials Processing Technology, vol. 88, 1999, pp.134-146.
 J.T. Oden and E.B. Pries, "Nonlocal and nonlinear friction law and variational principles for contact problems in elasticity," Trans. ASME : Journal of Applied Mechanics, vol. 50, 1983, pp.67-76.
 M.J. Saran and R.H. Wagoner, "A consistent implicit formulation for nonlinear finite element modeling with contact and friction. Part I. Theory,", Trans. ASME : Journal of Applied Mechanics, vol. 58, 1991, pp. 499-506.
 Y.M. Huang and D.K. Leu, "Finite element analysis of contact problems for a sheet metal bending process," Int. J. Computers and Structures, vol.57, 1996, pp.15-27.