Justification de la théorie non linéaire de Kirchhoff–Love,comme application d'une nouvelle méthode d'inversion singulière

In the framework of nonlinear elasticity, we consider a three-dimensional plate made of a St Venant–Kirchhoff isotropic and homogeneous material of thickness 2ε and periodic in the two other directions. By a change of scales, the problem can be mapped on a fixed open set, and seen as a nonlinear singular perturbation problem. We introduce a new singular inverse method. Applying this method, we prove that for fixed and small enough exterior forces, the three-dimensional displacement converges to the solution of the nonlinear Kirchhoff–Love theory of plate as the thickness 2ε tends to zero. The limit plate model contains in particular that of von Kármán. We also give a quantitative estimate of the convergence. To cite this article: R. Monneau, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 615–620.