On the axisymmetric Mindlin problem for a semi-space of granular material
type: Item
instance of: scholarly article
title: On the axisymmetric Mindlin problem for a semi-space of granular material
zbMATH Open document ID: 0606.73013
DOI: 10.1007/BF01184290
published in: Acta Mechanica
publication date: 1987-01-01T00:00:00Z
review text: The methods of images and Hankel transforms are used to construct solution to an axisymmetric boundary value problem of a semi-space of transversely isotropic (granular) material due to a point force applied at a distance h beneath its stress free plane boundary \(z=0\). Exact closed form expressions are determined for the components of displacements and stresses throughout the interior of the granular semi- space. The solution is then used to derive the surface displacements due to a uniformly distributed force over a circle of radius 'a' with centre at (0,0-h) in the plane \(z=-h\) of the semi-space. By a suitable choice of material constants and through a limit process as \(\alpha_ 1,\alpha_ 2\) approach 1, the granular semi-space becomes isotropic and the corresponding results derived in this particular case agree with those presented by \textit{I. Sneddon} [Fourier transforms (1951; Zbl 0038.268)].
Mathematics Subject Classification ID: 74E10
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 44A15
zbMATH DE Number: 3980592
zbMATH Keywords: axisymmetric Mindlin problem
zbMATH Keywords: methods of images
zbMATH Keywords: Hankel transforms
zbMATH Keywords: axisymmetric boundary value problem
zbMATH Keywords: semi-space
zbMATH Keywords: transversely isotropic (granular)
zbMATH Keywords: point force
zbMATH Keywords: Exact closed form expressions
zbMATH Keywords: components of displacements and stresses
zbMATH Keywords: surface displacements
author: Kashmiri L. Chowdhury
MaRDI profile type: Publication
cites work: Q4770618
cites work: Further criteria for elastic waves in anisotropic media
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description: scientific article; zbMATH DE number 3980592