End effects in anti-plane shear for an inhomogeneous isotropic linearly elastic semi-infinite strip
type: Item
instance of: scholarly article
title: End effects in anti-plane shear for an inhomogeneous isotropic linearly elastic semi-infinite strip
zbMATH Open document ID: 0941.74007
DOI: 10.1023/A:1007553422431
published in: Journal of Elasticity
publication date: 1999-11-23T00:00:00Z
review text: The equation \(\text{div}(A\nabla u)=0\) is studied under zero Dirichlet boundary conditions in the strip \(0<x_2 <h,\) \(x_1 >0\), where \(u\) is the shear displacement in the direction \(x_1\) of an inhomogeneous elastic body. It is assumed that \(A_{12}= A_{21}=0\), and \(A_{11} = A_{22}=\mu\). By setting \(w=\mu ^{1/2}u,\) the equation is reduced to the form \(\Delta w + Fw=0\), and the estimate \(|w|\leq k_1 \text{exp}(-k_2 x_1)\) is derived. Optimality of this estimate is discussed.
reviewed by: V. V. Shelukhin
Mathematics Subject Classification ID: 74B05
Mathematics Subject Classification ID: 35Q72
zbMATH DE Number: 1330600
zbMATH Keywords: linear inhomogeneous elasticity
zbMATH Keywords: optimal decay estimate
zbMATH Keywords: shear displacement
zbMATH Keywords: zero Dirichlet boundary conditions
zbMATH Keywords: boundary value problem
author: Albert M. Chan
author: Cornelius O. Horgan
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1330600