Rigorous construction of the dynamic equations of nonlinear theory of thin elastic plates
type: Item
instance of: scholarly article
title: Rigorous construction of the dynamic equations of nonlinear theory of thin elastic plates
zbMATH Open document ID: 0802.73034
DOI: 10.1007/BF01128926
author: Yu. N. Pronkin
published in: Computational Mathematics and Modeling
publication date: 1994-10-27T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74H45
zbMATH DE Number: 569822
zbMATH Keywords: perturbation method
zbMATH Keywords: method of Ciarlet-Raviart
zbMATH Keywords: leading terms
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: von Kármán's equations
zbMATH Keywords: inertial terms
reviewed by: A.Hanuška
MaRDI profile type: Publication
cites work: Q5548525
cites work: Solvability in the small of nonstationary problems for incompressible ideal and viscous fluids and the case of vanishing viscosity
cites work: Q3895818
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description: scientific article; zbMATH DE number 569822