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Justification of the nonlinear Kirchhoff-Love theory of plates as the application of a new singular inverse method. (English) Zbl 1030.74030
Summary: In the framework of isotropic homogeneous nonlinear elasticity for a St. Venant-Kirchhoff material, we consider a three-dimensional plate of thickness \(\varepsilon\) and periodic in two other directions. Using a new method that we call the singular inverse method, we prove the existence of a solution rescaled uniformly in \(\varepsilon\) for small forces, and at the same time, we prove the rigorous convergence of this rescaled solution to solution of the nonlinear Kirchhoff-Love plate model. We also state a \(3d-2d\) error estimate.

MSC:
74K20 Plates
74G20 Local existence of solutions (near a given solution) for equilibrium problems in solid mechanics (MSC2010)
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
35Q72 Other PDE from mechanics (MSC2000)
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