Integral form of the general solution of equations of steady-state thermoelasticity
type: Item
instance of: scholarly article
title: Integral form of the general solution of equations of steady-state thermoelasticity
zbMATH Open document ID: 0574.73008
DOI: 10.1016/0021-8928(84)90121-7
author: Yu. D. Kopeĭkin
author: V. P. Shishkin
published in: Journal of Applied Mathematics and Mechanics
publication date: 1985-01-01T00:00:00Z
review text: A new integral formula is obtained for solving the equation of steady- state thermoelasticity in a three-dimensional region, differing from the well-known formula [\textit{V. D. Kupradze}, \textit{T. G. Gegelia}, \textit{M. O. Basheleishvili} and \textit{T. V. Burchuladze}, Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity. Amsterdam, etc.: North-Holland (1979; Zbl 0406.73001)] in containing no volume integral. A similar formula is encountered in the case of a two-dimensional region, and its use in constructing the integral equation for boundary value problems is suggested. The fact that there are no volume integrals in the integral equations facilitates their numerical solution. If the temperature is represented by Green's formula in terms of the Newtonian potentials, of the single and double layer, and the mass force is conservative, then, as shown below, the volume integrals will also be transformed into surface integrals over the boundary surface. The resulting formula however is less suitable for the numerical solution of boundary value problem as it contains a large number of integrals with different kernels.
Mathematics Subject Classification ID: 74F05
zbMATH DE Number: 3917793
zbMATH Keywords: integral formula
zbMATH Keywords: equation of steady-state thermoelasticity
zbMATH Keywords: three- dimensional region
zbMATH Keywords: no volume integral
zbMATH Keywords: two-dimensional region
zbMATH Keywords: integral equation for boundary value problems
zbMATH Keywords: temperature
zbMATH Keywords: Green's formula
zbMATH Keywords: Newtonian potentials
zbMATH Keywords: single and double layer
zbMATH Keywords: mass force is conservative
zbMATH Keywords: large number of integrals with different kernels
MaRDI profile type: Publication
full work available at URL: 0021-8928(84)90121-7
OpenAlex ID: W2050725766
cites work: An advanced boundary integral equation method for three-dimensional thermoelasticity
description: scientific article; zbMATH DE number 3917793