# The conjugate problem of the thermal elasticity theory with imperfect heat contact between substances

Research output: Contribution to journalArticle

### Abstract

In this paper, the one-dimensional mathematical formulation of the conjugate coupling problem of the thermal elasticity theory with non-ideal contact between substances is suggested. The approximate analytical solution of the problem is received for both quasi-static and dynamic formulations. The integral transformation method of Laplace is used together with asymptotic representation of solution in the transformation space. The fields of the temperatures, stresses, strains and displacements are found. It is demonstrated with the help of some examples that the region near the interface may be the cause of the localization of stresses. The numerical solution of the quasi-static problem is in a qualitative agreement with the analytical estimations.

Original language English 252-260 9 Computational Materials Science 19 1-4 Published - 15 Dec 2000

### Fingerprint

Elasticity Theory
Imperfect
Elasticity
elastic properties
Heat
Contact
formulations
heat
integral transformations
Integral Transformation
Asymptotic Representation
Formulation
Laplace
causes
Analytical Solution
Numerical Solution
Temperature
temperature
Hot Temperature

### Keywords

• Analytical solution
• Coating
• Conjugate problem
• Coupling effect
• Heat resistance
• Thermoelasticity

### ASJC Scopus subject areas

• Materials Science(all)

### Cite this

In: Computational Materials Science, Vol. 19, No. 1-4, 15.12.2000, p. 252-260.

Research output: Contribution to journalArticle

@article{f9e1a81d9bf14206a77dd885c81da0e0,
title = "The conjugate problem of the thermal elasticity theory with imperfect heat contact between substances",
abstract = "In this paper, the one-dimensional mathematical formulation of the conjugate coupling problem of the thermal elasticity theory with non-ideal contact between substances is suggested. The approximate analytical solution of the problem is received for both quasi-static and dynamic formulations. The integral transformation method of Laplace is used together with asymptotic representation of solution in the transformation space. The fields of the temperatures, stresses, strains and displacements are found. It is demonstrated with the help of some examples that the region near the interface may be the cause of the localization of stresses. The numerical solution of the quasi-static problem is in a qualitative agreement with the analytical estimations.",
keywords = "Analytical solution, Coating, Conjugate problem, Coupling effect, Heat resistance, Thermoelasticity",
author = "Knyazeva, {A. G.}",
year = "2000",
month = "12",
day = "15",
language = "English",
volume = "19",
pages = "252--260",
journal = "Computational Materials Science",
issn = "0927-0256",
publisher = "Elsevier",
number = "1-4",

}

TY - JOUR

T1 - The conjugate problem of the thermal elasticity theory with imperfect heat contact between substances

AU - Knyazeva, A. G.

PY - 2000/12/15

Y1 - 2000/12/15

N2 - In this paper, the one-dimensional mathematical formulation of the conjugate coupling problem of the thermal elasticity theory with non-ideal contact between substances is suggested. The approximate analytical solution of the problem is received for both quasi-static and dynamic formulations. The integral transformation method of Laplace is used together with asymptotic representation of solution in the transformation space. The fields of the temperatures, stresses, strains and displacements are found. It is demonstrated with the help of some examples that the region near the interface may be the cause of the localization of stresses. The numerical solution of the quasi-static problem is in a qualitative agreement with the analytical estimations.

AB - In this paper, the one-dimensional mathematical formulation of the conjugate coupling problem of the thermal elasticity theory with non-ideal contact between substances is suggested. The approximate analytical solution of the problem is received for both quasi-static and dynamic formulations. The integral transformation method of Laplace is used together with asymptotic representation of solution in the transformation space. The fields of the temperatures, stresses, strains and displacements are found. It is demonstrated with the help of some examples that the region near the interface may be the cause of the localization of stresses. The numerical solution of the quasi-static problem is in a qualitative agreement with the analytical estimations.

KW - Analytical solution

KW - Coating

KW - Conjugate problem

KW - Coupling effect

KW - Heat resistance

KW - Thermoelasticity

UR - http://www.scopus.com/inward/record.url?scp=0347368407&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347368407&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0347368407

VL - 19

SP - 252

EP - 260

JO - Computational Materials Science

JF - Computational Materials Science

SN - 0927-0256

IS - 1-4

ER -