Rigorous construction of the dynamic equations of nonlinear theory of thin elastic plates
Using the method of Ciarlet-Raviart, the geometrically nonlinear plates are investigated. It is shown that the leading terms in the asymptotic expansion of the three-dimensional dynamic nonlinear equations represent a dynamical analogy of the von Kármán's equations. The inertial terms corresponding with the displacements of the plate middle surface are of higher order than those of the transversal bending and may be neglected.
scientific article; zbMATH DE number 569822