On small finite deflections of sheardeformable elastic plates
type: Item
instance of: scholarly article
title: On small finite deflections of sheardeformable elastic plates
zbMATH Open document ID: 0595.73032
DOI: 10.1016/0045-7825(86)90103-9
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1986-01-01T00:00:00Z
review text: We are concerned in what follows with a tenth-order system of differential equations which, in a certain sense, may be thought of as a limit of possible generalizations, including the effect of transverse sheardeformability, of von Kármán's equations for isotropic nonsheardeformable plates. We show that, subject to certain restrictions, this system of equations can be written, in direct extension of von Kármán's result and in direct extension of a special case of a recent result of sheardeformable shallow shells [the author and \textit{F. Y. M. Wan}, Z. Angew. Math. Phys. 33, 425-427 (1982; Zbl 0485.73055)], in the form of two simultaneous fourth-order equations supplemented by one equation of second order. We further establish contact with our original formulation of a variational equation for stresses and displacements within the framework of small finite deflection plate theory [the author, J. Math. Phys. 32, 129-135 (1953; Zbl 0051.163)], and we transform the present generalized version of this earlier result in a manner which is related to a very recent consideration of a mixed variational equation for displacements and transverse stresses in three-dimensional elastic layers [the author, Int. J. Numer. Methods Eng. 23, 193-198 (1986; Zbl 0579.73018)]. With this we then formulate a mixed variational equation with the property that it's Euler equations come out to be just that system of equations which we here consider the limit of possible generalizations of von Kármán's equations.
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 35A15
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 74S30
zbMATH DE Number: 3958839
zbMATH Keywords: reduction procedure
zbMATH Keywords: uniform, homogeneous, constitutively linear
zbMATH Keywords: orthotropic plates
zbMATH Keywords: uniform, homogeneous isotropic plates
zbMATH Keywords: tenth-order system of differential equations
zbMATH Keywords: transverse sheardeformability
zbMATH Keywords: isotropic nonsheardeformable plates
zbMATH Keywords: two simultaneous fourth-order equations
zbMATH Keywords: one equation of second order
zbMATH Keywords: small finite deflection
zbMATH Keywords: displacements
zbMATH Keywords: transverse stresses
zbMATH Keywords: mixed variational equation
zbMATH Keywords: generalizations of von Kármán's equations
author: Eric Reissner
MaRDI profile type: Publication
full work available at URL: 0045-7825(86)90103-9
OpenAlex ID: W2030322780
cites work: On a Variational Theorem for Finite Elastic Deformations
cites work: On the theory of transverse bending of elastic plates
cites work: On a mixed variational theorem and on shear deformable plate theory
cites work: A note on the linear theory of shallow shear-deformable shells
description: scientific article; zbMATH DE number 3958839