On the theory of thick slabs on an elastic foundation
type: Item
instance of: scholarly article
title: On the theory of thick slabs on an elastic foundation
zbMATH Open document ID: 0628.73126
DOI: 10.1016/0021-8928(86)90105-X
author: B. George
published in: Journal of Applied Mathematics and Mechanics
publication date: 1986-01-01T00:00:00Z
review text: Static problems are investigated covering the deformation of a thick elastic slab with an arbitrary smooth boundary that rests without friction on a linearly deformable foundation. The slab is loaded by a normal distributed load on the upper face. Lur'e's symbolic method is used to investigate the state of stress and strain of the slab. A class of homogeneous solutions corresponding to a free upper face and the condition of linear elastic-contact of the slab with the foundation on the lower face of the slab is isolated. This last condition is a relation realized by the integral operator of the contact problem for a linearly deformable foundation between the settling of the slab and the contact stress. It is shown that the homogeneous solution determined in this manner can be of three kinds: potential, vortical, and harmonic. There is also a certain elementary solution. The problem here of finding the characteristic numbers of the potential solution reduces to seeking the eigenvalues of the integral operator mentioned. The axisymmetric problem of the deformation of a thick circular slab in a Winkler foundation is considered as an example.
Mathematics Subject Classification ID: 74A55
Mathematics Subject Classification ID: 74M15
zbMATH DE Number: 4022829
zbMATH Keywords: two-dimensional Fredholm integral equation of second kind
zbMATH Keywords: Static problems
zbMATH Keywords: thick elastic slab
zbMATH Keywords: arbitrary smooth boundary
zbMATH Keywords: linearly deformable foundation
zbMATH Keywords: Lur'e's symbolic method
zbMATH Keywords: homogeneous solutions
zbMATH Keywords: linear elastic-contact
zbMATH Keywords: potential
zbMATH Keywords: vortical
zbMATH Keywords: harmonic
zbMATH Keywords: characteristic numbers of the potential solution
zbMATH Keywords: eigenvalues of the integral operator mentioned
MaRDI profile type: Publication
cites work: Q5530635
cites work: Eigenfunction Solution for Beam on Elastic Foundation
cites work: Q5544938
cites work: Method of orthogonal functions in mixed problems of continuum mechanics
cites work: The state op stress in a thick plate
full work available at URL: 0021-8928(86)90105-x
OpenAlex ID: W2078385308
description: scientific article; zbMATH DE number 4022829