Archive for Rational Mechanics and Analysis

, Volume 73, Issue 4, pp 349–389

A justification of the von Kármán equations

  • Philippe G. Ciarlet

DOI: 10.1007/BF00247674

Cite this article as:
Ciarlet, P.G. Arch. Rational Mech. Anal. (1980) 73: 349. doi:10.1007/BF00247674


The method of asymptotic expansions, with the thickness as the parameter, is applied to the nonlinear, three-dimensional, equations for the equilibrium of a special class of elastic plates under suitable loads. It is shown that the leading term of the expansion is the solution of a system of equations equivalent to those of von Kármán. The existence of solutions of this system is established. It is also shown that the displacement and stress corresponding to the leading term of the expansion have the specific form generally assumed in the usual derivations of the von Kármán equations; in particular, the displacement field is of Kirchhoff-Love type. This approach also clarifies the nature of admissible boundary conditions for both the von Kármán equations and the three-dimensional model from which these equations are obtained. A careful discussion of the limitations of this approach is given in the conclusion.

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Philippe G. Ciarlet
    • 1
  1. 1.Analyse Numérique Tour 55-65 Université Pierre et Marie CurieParis

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