A new quasilinear model for plate buckling

Journal of Elasticity

Volumn 71, Issue 1-3, 2003, Pages 157-182

  Podio Guidugli, Paolo ^a  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

Nonlinear eigenvalue problems; Plate buckling; Von K rm n equations

Indexed keywords

APPROXIMATION THEORY; BUCKLING; EIGENVALUES AND EIGENFUNCTIONS; LINEARIZATION; MATHEMATICAL MODELS; PLATES (STRUCTURAL COMPONENTS); PROBLEM SOLVING;

NONLINEAR EIGENVALUE PROBLEM; PLATE BUCKLING; QUASILINEAR MODEL; VON KARMAN EQUATION;

ELASTICITY;

EID: 0348233517     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:ELAS.0000005554.76200.9e     Document Type: Article

References (21)

1. S.S. Antman, Nonlinear Problems of Elasticity. Springer, Berlin (1995).
2. M.S. Berger, Nonlinearity and Functional Analysis. Academic Press, New York (1977).
3. S. Chow and J. Hale, Methods of Bifurcation Theory. Springer, Berlin (1996).
4. P.G. Ciarlet, A justification of the von Kármán equations. Arch. Rational Mech. Anal. 73 (1980) 349-389.
5. P.G. Ciarlet, Plates and Junctions in Elastic Multi-Structures: An Asymptotic Analysis. Springer, Berlin (1990).
6. P.G. Ciarlet, Mathematical Elasticity, Vol. II: Theory of Plates. North-Holland, Amsterdam (1997).
7. M.G. Crandall and P.H. Rabinowitz, Nonlinear Sturm-Liouville eigenvalue problems and topological degree. J. Math. Mech. 19 (1970) 1083-1102.
8. J.L. Davet, Justification de modèles de plaques non linéaires pour des lois des comportements générales. Moddél. Math. Anal. Numér. 20 (1986) 225-249.
9. D.D. Fox, A. Raoult and J.C. Simo, A justification of nonlinearly properly invariant plate theories. Arch. Rational Mech. Anal. 124 (1993) 157-199.
10. G. Friesecke, R.D. James and S. Müller. A theorem of geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity. Comm. Pure Appl. Math. LV (2002) 1461-1506.
11. G. Friesecke, R.D. James and S. Müller, The Föppl-von Kármán plate theory as a low energy Gamma limit of nonlinear elasticity. C. R. Math. Acad. Sci. Paris 335 (2002) 201-206.
12. M.E. Gurtin, The linear theory of elasticity. In: S. Flügge (ed.), Handbuch der Physik Via/2. Springer, Berlin (1972).
13. M.E. Gurtin and P. Podio-Guidugli, The thermodynamics of constrained materials. Arch. Rational Mech. Anal. 51 (1973) 192-208.
14. T.J. Healey and H.C. Simpson, Global continuation in nonlinear elasticity. Arch. Rational Mech. Anal. 143 (1998) 1-28.
15. P.M. Naghdi and R.P. Nordgren, On the nonlinear theory of elastic shells under the Kirchhoff hypothesis. Quart. Appl. Math. 21 (1963) 49-59.
16. P. Podio-Guidugli, An exact derivation of the thin plate equation. J. Elasticity 22 (1989) 121-133.
17. P. Podio-Guidugli, A Primer in Elasticity. Kluwer Academic Publishers, Dordrecht (2000).
18. P.H. Rabinowitz, Some global results for nonlinear eigenvalue problems. J. Funct. Anal. 7 (1971) 487-513.
19. C. Truesdell, Some challenges offered to analysis by rational thermodynamics. In: G.M. de la Penha and L.A. Medeiros (eds), Contemporary Developments in Continuum Mechanics and Partial Differential Equations. North-Holland, Amsterdam (1978)
20. C. Truesdell and W. Noll, The non-linear field theories of mechanics. In: S. Flügge (ed.), Handbuch der Physik, Vol. III/3. Springer, Berlin (1965).
21. T. von Kármán, Festigkeitsprobleme in Maschinenbau. In: F. Klein and C. Müller (eds), Encyclopädie der Matematisches Wissenschaften, Vol. IV/4. Teubner, Stuttgart (1910) pp. 311-385.