Numerical solutions of the Von Karman equations for a thin plate

International Journal of Modern Physics C

Volumn 8, Issue 2, 1997, Pages 427-434

  Da Silva, Pedro Patrício ^a   Krauth, Werner ^a  

^a CNRS   (France)

Author keywords

Finite Element Method; Large Dimensional Minimization; Nonlinear Elasticity; Plate Mechanics; Von Karman Equations

Indexed keywords

EID: 0347702275     PISSN: 01291831     EISSN: None     Source Type: Journal    
DOI: 10.1142/s0129183197000357     Document Type: Article

References (12)

1. L. D. Landau and E. M. Lifshitz, Theory of Elasticity - Course of Theoretical Physics, Vol. 7 (Pergamon Press, 1954).
2. H. R. Schwarz, Finite Element Methods (Academic Press, 1988).
3. The integrals, which are all polynomials in s and t, can be computed exactly by Gaussian integration.
4. Most of the work has dealt with the theory of plates in the limit of small linear deformations. For large deformations, a spring model has been used within a boundary layer analysis (A. E. Lobkovsky, Phys. Rev. E53, 3750 (1996). Cf. also T. Hughes et al. (Eds.), Finite Element Methods for Plate and Shell Structures (Pineridge Press International, Swansea, U.K., 1986) , and M. Bernadou, Méthodes d'Eléments finis pour les Problèmes de Coques minces (Masson, 1994) who discuss several finite element approximations of the nonlinear problem for plate and shell theories.
5. Most of the work has dealt with the theory of plates in the limit of small linear deformations. For large deformations, a spring model has been used within a boundary layer analysis (A. E. Lobkovsky, Phys. Rev. E53, 3750 (1996). Cf. also T. Hughes et al. (Eds.), Finite Element Methods for Plate and Shell Structures (Pineridge Press International, Swansea, U.K., 1986) , and M. Bernadou, Méthodes d'Eléments finis pour les Problèmes de Coques minces (Masson, 1994) who discuss several finite element approximations of the nonlinear problem for plate and shell theories.
6. Most of the work has dealt with the theory of plates in the limit of small linear deformations. For large deformations, a spring model has been used within a boundary layer analysis (A. E. Lobkovsky, Phys. Rev. E53, 3750 (1996). Cf. also T. Hughes et al. (Eds.), Finite Element Methods for Plate and Shell Structures (Pineridge Press International, Swansea, U.K., 1986) , and M. Bernadou, Méthodes d'Eléments finis pour les Problèmes de Coques minces (Masson, 1994) who discuss several finite element approximations of the nonlinear problem for plate and shell theories.
7. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge University Press, 1992).
8. G. H. Golub and C. F. van Loan, Matrix Computations (Johns Hopkins University Press, 1989), Chap. 10.3.
9. Due to numerical problems in determining H and its eigensystem for the very bad conditioning encountered, the new Hessian H̃ is usually not very close to the unity matrix. The reconditioning can be iterated at the same point. The expense of doing this has to be weighted against the fact that H, of course, depends on ξ.
10. In both cases, we impose the symmetries x → - x, y → - y of the solution.
11. I. Babuska, Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations (Springer-Verlag, 1995).
12. M. Ben Amar and Y. Pomeau, Proc. Roy. Soc. (to appear).