Nonlinear equations of elastic deformation of plates
type: Item
instance of: scholarly article
zbMATH Open document ID: 1001.74010
author: A. E. Alekseev
publication date: 2001-12-13T00:00:00Z
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74K20
zbMATH DE Number: 1682302
zbMATH Keywords: Legendre polynomials
zbMATH Keywords: approximation of Hook's law
zbMATH Keywords: linearized equation
MaRDI profile type: Publication
title: Nonlinear equations of elastic deformation of plates
published in: Prikladnaya Mekhanika i Tekhnicheskaya Fizika
review text: A method for constructing nonlinear equations of elastic deformation of plates with boundary conditions for stresses and displacements at the face surfaces in an arbitrary coordinate system is proposed. The initial three-dimensional problem of the nonlinear theory of elasticity is reduced to a one-parameter sequence of two-dimensional problems by approximating the unknown functions by truncated series in Legendre polynomials. The same unknowns are approximated by different truncated series. In each approximation, a linearized system of equations whose differential order does not depend on the boundary conditions at the face surfaces which can be formulated in terms of stresses or displacements is obtained.
description: scientific article; zbMATH DE number 1682302