Asymptotic solution of a quasistatic thermoelaticity problem for a slender rod
type: Item
instance of: scholarly article
title: Asymptotic solution of a quasistatic thermoelaticity problem for a slender rod
zbMATH Open document ID: 0677.73011
DOI: 10.1016/0021-8928(87)90138-9
author: V. F. Butuzov
author: T. A. Urazgil'dina
published in: Journal of Applied Mathematics and Mechanics
publication date: 1987-01-01T00:00:00Z
review text: The authors consider a boundary value problem of quasistatic linear thermoelasticity for a thin round rod whose radius is equal to \(\epsilon\) b and whose length is equal to a. Cylindrical coordinates (\(\rho\),\(\psi\),z) are used. Conditions on the lateral boundary of the rod are: \(v=\epsilon \psi (z,t,\epsilon)\), \(\partial W/\partial \rho =0\), \((\partial \theta /\partial \rho)+A\epsilon \theta =0\); and on the edges of the rod are: \(z=ia:\) \((\partial W/\partial \rho)+(\partial v/\partial z)=0\), \(W=\psi_ i(\rho,t)\), \(\theta =\mu_ i(\rho,t)\), \(i=0;1.\) The asymptotic form of the solution, as \(\epsilon\) \(\to 0\), is constructed using a traditional method. Boundary-layers solutions are used which are combined with the regular part of the solution. An asymptotic form of the solution, as time t tends to 0, is taken into account, too. The asymptotic is justified. Under some conditions the existence theorem for the problem is proven. By using the previous results a one-dimensional model of the thermoelastic rod is proposed.
Mathematics Subject Classification ID: 74F05
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35C20
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 74H99
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 74A15
Mathematics Subject Classification ID: 74K10
zbMATH DE Number: 4110222
zbMATH Keywords: boundary-function method
zbMATH Keywords: linear thermoelasticity
zbMATH Keywords: existence theorem
zbMATH Keywords: one-dimensional model
reviewed by: Leonid Lebedev
MaRDI profile type: Publication
full work available at URL: 0021-8928(87)90138-9
OpenAlex ID: W2087203296
cites work: Q5634929
cites work: Q4139051
cites work: Q3205645
cites work: Asymptotic solution of the problem concerning the propagation of heat in thin bodies
description: scientific article; zbMATH DE number 4110222