Optimum Design of the Process Parameter in Sheet Metal Forming with Design Sensitivity Analysis using the Direct Differentiation Approach (I) -Design Sensitivity Analysis-

직접미분 설계민감도 해석을 이용한 박판금속성형 공정변수 최적화 (I) -설계민감도 해석 -

  • 김세호 (현대자동차(주) 선행해석팀) ;
  • 허훈 (한국과학기술원 기계공학과)
  • Published : 2002.11.01


Design sensitivity analysis scheme is proposed in an elasto -plastic finite element method with explicit time integration using a direct differentiation method. The direct differentiation is concerned with large deformation, the elasto-plastic constitutive relation, shell elements with reduced integration and the contact scheme. The design sensitivities with respect to the process parameter are calculated with the direct analytical differentiation of the governing equation. The sensitivity results obtained from the present theory are compared with that obtained by the finite difference method in a class of sheet metal forming problems such as hemi-spherical stretching and cylindrical cup deep-drawing. The result shows good agreement with the finite difference method and demonstrates that the preposed sensitivity calculation scheme is a pplicable in the complicated sheet metal forming analysis and design.


Elasto-plastic Finite Element Method;Design Sensitivity Analysis;Sheet Metal Forming Process


  1. Simo, J. C. and Taylor, R. L., 1986, 'A Return Mapping Algorithm for Plane Stress Elasto-plasticity,' Int. J. Numer. Meth. Engng., Vol. 22, pp. 649 - 670
  2. Chen, X., 1994, Nonlinear Finite Element Sensitivity Analysis for Large Deformation Elasto-plastic and Contact Problems, Ph. D. Dissertation, University of Tokyo
  3. Makinouchi, A., Nakamachi, E., Onate, E. and Wagoner, R. H., 1993, Proceedings of the 2nd International Conference NUMISHEET'93, Ishihara
  4. Yang, J. B., Jeon, B. H. and Oh, S. I., 2001, 'Design Sensitivity Analysis and Optimization of the Hydroforming Process,' J Mater. Process. Technol., Vol. 113, pp. 666 - 672
  5. Belytschko, T., Lin, J. I. and Tsay, C., 1984, 'Explicit Algorithms for the Nonlinear Dynamics of Shells,' Comput. Methods Appl. Mech. Engrg., Vol. 42, pp. 225 - 251
  6. Flanagan, D. and Belytschko, T., 1981, 'A Uniform Strain Hexahedron and Quadrilateral with Orthogonal Hourglass Control,' Int. J. Numer. Meth. Engng., Vol. 17,pp.679-706
  7. Hill, R., 1950, The Mathematical Theory of Plasticity, Oxford, Claredon Press
  8. Lee, T. H. and Arora, J. S., 1995, 'A Computational Method for Design Sensitivity Analysis of Elastoplastic Structures,' Comput. Methods Appl. Mech. Engrg., Vol. 122, pp. 27-50.
  9. Cho, S. and Choi, K. K., 2000, 'Design Sensitivity Analysis and Optimization of Non-linear Transient Dynamics. Part II-Configuration Design,' Int. J. Numer. Meth. Engng., Vol. 48, pp. 375 -399<375::AID-NME879>3.0.CO;2-8
  10. Zabaras, N., Bao, Y., Srikanth, A. and Frazier, W. G., 2000, 'A Continuum Lagrangian Sensitivity Analysis for Metal Forming Processes with Application to Die Design Problems,' Int. J. Numer. Meth. Engng., Vol. 48, pp. 679-720<679::AID-NME895>3.0.CO;2-U
  11. Ghouati, O. and Gelin, J. C., 1998, 'Sensitivity Analysis in Forming Processes,' Int. J. Forming Processes, Vol. 1, pp. 297-322
  12. Kleiber, M., Antunez, H., Hien, T. D. and Kowalczyk, P., 1997, Parameter Sensitivity in Nonlinear Mechanics - Theory and Finite Element Computations, John Wiley & Sons Ltd, Chichester