Boussinesq's problem for a debonded boundary
type: Item
instance of: scholarly article
title: Boussinesq's problem for a debonded boundary
zbMATH Open document ID: 0683.73059
DOI: 10.1007/BF00945306
author: M. C. Au
author: A. P. S. Selvadurai
author: B. M. Singh
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1989-01-01T00:00:00Z
review text: In the cylindrical coordinates system the following axially-symmetric mixed boundary-value problem is consideed: \(u_ z(r,0)=\Delta\), \(0\leq r\leq a\); \(\sigma_{rz}(r,0)=0\), \(0<r<b\); \(\sigma_{zz}(r,0)=0\), \(a<r<b\); \(u_ r(r,0)=0\), \(b\leq r<\infty\); \(u_ z(r,0)=0\), \(b\leq r<\infty\). The presented solution aims to deal with the physical problem as follows: 1. An elastic isotropic half-space is bounded symmetrically along the boundary \(b\leq r<\infty\) and debonded in the region \(0\leq r\leq b\)- a crack region. 2. A rigid cylindrical punch of the radius a is applied symmetrically in the crack plane. A rather complicated solution involving the Hankel transforms technique and integral equations is presented, with well known weaknesses at the boundaries \(r=a\) and \(r=b\) (oscillatory singularity and overlapping displacement). The main result - the derived load-displacement relationship seems to be of a sufficient accuracy and of some practical use.
Mathematics Subject Classification ID: 74A55
Mathematics Subject Classification ID: 74M15
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 74H99
Mathematics Subject Classification ID: 74R05
Mathematics Subject Classification ID: 45B05
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 4119772
zbMATH Keywords: debonded interface
zbMATH Keywords: indentation problem
zbMATH Keywords: Abel-type integral equation
zbMATH Keywords: force-displacement relationship
zbMATH Keywords: axially-symmetric mixed boundary-value problem
zbMATH Keywords: rigid cylindrical punch
zbMATH Keywords: Hankel transforms technique
zbMATH Keywords: load- displacement relationship
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4119772