Journal of Mechanical Science and Technology

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지

General Asymptotic Formulation for the Bifurcation Problem of Thin Walled Structures in Contact with Rigid Surfaces

  • Published : 2000.01.01
Download PDF
⟨ Previous Next ⟩

Abstract

The bifurcation problem of thin walled structures in contact with rigid surfaces is formulated by adopting the multiple scales asymptotic technique. The general theory developed in this paper is very useful for the bifurcation analysis of waviness instabilities in the sheet metal forming. The formulation is presented in a full Lagrangian formulation. Through this general formulation, the bifurcation functional is derived within an error of O($(E^4)$) (E: shell's thickness parameter). This functional can be used in numerical solutions to sheet metal forming instability problem.

Keywords

References

  1. Bensoussan, A., Lions, J. L. and Papanicolaou, G., 1978, Asymptotic Analysis for Periodic Structures, North Holland
  2. Destuynder, der, P., 1980, 'On the Justification of Plate and Shell Models,' (in French) Doc. Thesis, Univ. of Paris VI
  3. Devons, J. D., 1941, The Methodology of Deep Drawing & Pressing, Chapman Hall, London
  4. Donoghue, M., Stevenson, R., Kwon, Y. J. and Triantafyllidis, N., 1989, 'An Experimental Verification of the Hemispherical Cup Puckering Problem,' J. of Engineering Materials and Technology Vol. 111, pp. 248 - 254
  5. Hill, R., 1957, 'On Uniqueness and Stability in the Theory of Finite Elastic Strain,' J. of the Mechanics and Physics of Solids Vol. 5, pp. 229 - 241
  6. Hill, R., 1958, 'A General Theory of Uniqueness and Stability in Elastic-Plastic Solids,' J. of the Mechanics and Physics of Solids Vol. 6, pp. 236-249
  7. Hutchinson, J. W., 1974, 'Plastic Buckling,' Adv. Appl Mech. Vol. 14 (Edited by C. S. Yih), Academic Press, New York, pp. 67 -145
  8. Kim, Y. S., Son, Y. J. and Park, J. Y., 1999, 'Bifurcation Analysis of Wrinkling Formation for Anisotropic Sheet,' KSME International Journal Vol. 13 No.3, pp. 221-228
  9. Koiter, W. T., 1945, 'On the Stability of Elastic Equilibrium,' (in Dutch), Doc. Thesis, Delft University Amsterdam
  10. Kwon, Y. J., 1992, 'Buckling Theory in Solid Structure with Small Thickness (Part 1) - General Formulation of Problem -,' KSME Journal Vol. 6 No.2, pp. 109-113
  11. Kwak, B. M., 1990, 'Numerical Implementation of Three-Dimensional Frictional Contact by a Linear Complementarity Problem,' KSME Journal Vol. 4 No.1, pp. 23-31
  12. Oden, J. T. and Pires, E. B., 1983, 'Nonlocal and Nonlinear Friction Laws and Variational Principles for Contact Problems in Elasticity,' J. of Applied Mechanics Vol. 50, pp. 67 -76
  13. Triantafyllidis, N. and Kwon, Y. J., 1987, 'Thickness Effects on the Stability of Thin Walled Structures,' J. of the Mechanics and Physics of Solids Vol. 35 No.5, pp. 643-674
  14. Triantafyllidis, N., 1980, 'Bifurcation Phenomena in a Pure Bending,' J. of the Mechanics and Physics of Solids Vol. 28, pp. 221- 245
  15. Triantafyllidis, N. and Needleman, A., 1980, 'An Analysis of Wrinkling in the Swift Cup Test,' J. of the Engineering Materials and Technology Vol. 102, pp. 241- 256