The von Karman equations, the stress function, and elastic ridges in high dimensions

Journal of Mathematical Physics

Volumn 38, Issue 2, 1997, Pages 830-846

  Kramer, Eric M ^a  

^a UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031541686     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.531893     Document Type: Article

References (30)

1. E. M. Kramer and T. A. Witten, submitted to Phys. Rev. Lett.
2. F. Plouraboue and S. Roux, Physica A 227, 173 (1996).
3. R. E. Newton, in 7th International Technical Conference on Experimental Safety Vehicles (U.S. Dept. of Transportation, Washington, DC, 1980).
4. E. M. Kramer and A. E. Lobkovsky, Phys. Rev. E 53, 1465 (1995).
5. T. A. Witten and H. Li, Europhys. Lett. 23, 51 (1996).
6. A. E. Lobkovsky, Phys. Rev. E 53, 3750 (1996).
7. A. E. Lobkovsky et al., Science 270, 1482 (1995).
8. Surprisingly, the leading corrections to the ridge are not confined. See Ref. 23.
9. E. M. Kramer and T. A. Witten, to be submitted to Phys. Rev. E.
10. Statistical Mechanics of Membranes and Surfaces, edited by D. Nelson, T. Piran, and S. Weinberg (World Scientific, Singapore, 1989).
11. M. Paczuski, M. Kardar, and D. Nelson, Phys. Rev. Lett. 60, 2638 (1988).
12. E. Guitter, F. David, S. Leibler, and L. Peliti, J. Phys. France 50, 1787 (1989).
13. A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity (Dover, New York, 1944).
14. L. Landau and E. Lifshitz, Theory of Elasticity (Pergarion, New York, 1959).
15. The Theory of Thin Elastic Shells, edited by W. T. Koiter (North-Holland, New York, 1960).
16. M. Dikmen, Theory of Thin Elastic Shells (Pitman, Boston, 1982). See in particular pp. 156-157 and references therein for a discussion of convergence questions.
17. J. E. Lagnese, Boundary Stabilization of Thin Plates (SIAM, Philadelphia, 1989).
18. T. von Karman, The Collected Works of Theodore von Karman (Butterworths, London, 1956), Vol. 1, p. 176.
19. G. B. Airy, Philos. Trans. R. Soc. 153, 49 (1863). See also the historical introduction in Ref. 13.
20. H. S. Seung and D. R. Nelson, Phys. Rev. A 38, 1005 (1988).
21. J. C. Maxwell, Edinburgh R. Soc. Trans. 26 (1870), reprinted in The Scientific Papers of James Clerk Maxwell (Cambridge University Press, Cambridge, 1927), Vol. 2, p. 161.
22. J. C. Maxwell, Edinburgh R. Soc. Trans. 26 (1870), reprinted in The Scientific Papers of James Clerk Maxwell (Cambridge University Press, Cambridge, 1927), Vol. 2, p. 161.
23. H. Kleinert, Gauge Fields in Condensed Matter (World Scientific, London, 1989).
24. A. E. Lobkovsky and T. A. Witten, to appear in Phys. Rev. E.
25. L. P. Eisenhart, Differential Geometry (Ginn and Company, New York, 1909).
26. R. S. Millman and G. D. Parker, Elements of Differential Geometry (Prentice-Hall, Englewood Cliffs, NJ, 1977).
27. B. Schutz, A First Course in General Relativity (Cambridge University Press, Cambridge, 1988).
28. M. Abromowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
29. See sections 11-14 of Ref. 14 for a complete treatment of a thin plate in the Monge representation.
30. αβ.