Generalized von Karman equations

In a previous work, the first author has identified three-dimensional boundary conditions "of von Karman's type" that lead, through a formal asymptotic analysis of the three-dimensional solution, to the classical von Karman equations, when they are applied to the entire lateral face of a nonlinearly elastic plate. In this Note, we consider the more general situation where only a portion of the lateral face is subjected to boundary conditions of von von Karman's type, while the remaining portion is subjected to boundary conditions of free edge. We then show that the asymptotic analysis of the three-dimensional solution still leads in this case to a two-dimensional boundary value problem that is analogous to the von Karman equations. In particular, the boundary conditions for the Airy function can still be determined solely from the data. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.