Axisymmetric problem of a nonhomogeneous elastic layer
type: Item
instance of: scholarly article
title: Axisymmetric problem of a nonhomogeneous elastic layer
zbMATH Open document ID: 0920.73033
author: S. H. Smith
published in: Archive of Applied Mechanics
publication date: 1999-09-19T00:00:00Z
review text: The paper is devoted to the elastic behaviour of nonhomogeneous materials defined by the relation \(G(\overline z)= G_0\overline z^m\), i.e. the shear modulus of elasticity \(G\) varies with the power of the dimensionless axial coordinate \(\overline z\). The fundamental differential equation governing such nonhomogeneous medium was proposed by \textit{K. M. Kassir} in [Proc. of the ASCE, Mechanic Division 98, 457-470 (1972)]. Here the authors show that these fundamental equations are not sufficient for formulating several types of boundary value problems. It is shown in this paper that fundamental equations derived in an earlier paper [J. Thermal stress. 5, No. 1, 1-11 (1982)] can be used to formulate axisymmetric problems for a thick plate subjected to an arbitrary distributed load or a concentrated load on its surface. Numerical calculations are made for several values of the non-homogeneous parameter \(m\), and numerical variations of stress and displacement components are shown graphically.
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 74H99
Mathematics Subject Classification ID: 74K20
zbMATH DE Number: 1192774
zbMATH Keywords: shear modulus of elasticity
zbMATH Keywords: dimensionless axial coordinate
zbMATH Keywords: thick plate
zbMATH Keywords: arbitrary distributed load
zbMATH Keywords: concentrated load
MaRDI profile type: Publication
full work available at URL: s004190050143
OpenAlex ID: W2077755720
DOI: 10.1007/S004190050143
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description: scientific article; zbMATH DE number 1192774