Justification of the nonlinear Kirchhoff-Love theory of plates as the application of a new Singular Inverse Method

摘要

In the framework of isotropic homogeneous nonlinear elasticity for a St. Venant-Kirchhoff material, we consider a three-dimensional plate of thickness epsilon and periodic in the two other directions. Using a new method that we call the Singular Inverse Method, we prove the existence of a solution rescaled uniformly in epsilon for small forces, and at the same time, we prove the rigorous convergence of this rescaled solution to the solution of the nonlinear Kirchhoff-Love plate model. We also state a 3d-2d error estimate. [References: 28]