Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-28T15:19:30.008Z Has data issue: false hasContentIssue false
  • English
  • Français

Thermal Stress Analysis of 3D Anisotropic Materials Involving Domain Heat Source by the Boundary Element Method

Published online by Cambridge University Press:  04 November 2019

Y. C. Shiah Open the ORCID record for Y. C. Shiah [Opens in a new window] ,
Nguyen Anh Tuan  and
M.R. Hematiyan
Y. C. Shiah*
Affiliation:
Department of Aeronautics and AstronauticsNational Cheng Kung UniversityTainan, Taiwan, R.O.C.
Nguyen Anh Tuan
Affiliation:
Department of Aeronautics and AstronauticsNational Cheng Kung UniversityTainan, Taiwan, R.O.C.
M.R. Hematiyan
Affiliation:
Department of Mechanical EngineeringShiraz University, Shiraz, Iran
*
*Corresponding author ([email protected])
Get access

Abstract

In engineering applications, it is pretty often to have domain heat source involved inside. This article proposes an approach using the boundary element method to study thermal stresses in 3D anisotropic solids when internal domain heat source is involved. As has been well noticed, thermal effect will give rise to a volume integral, where its direct evaluation will need domain discretization. This shall definitely destroy the most distinctive notion of the boundary element method that only boundary discretization is required. The present work presents an analytical transformation of the volume integral in the boundary integral equation due to the presence of internal volume heat source. For simplicity, distribution of the heat source is modeled by a quadratic function. When needed, the formulations can be further extended to treat higher-ordered volume heat sources. Indeed, the present work has completely restored the boundary discretization feature of the boundary element method for treating 3D anisotropic thermoelasticity involving volume heat source.

Keywords

Boundary element methodthree-dimensional anisotropic thermoelasticityquadratic volume heat source
Type
Research Article
Information
Journal of Mechanics , Volume 35 , Issue 6 , December 2019 , pp. 839 - 850
Copyright
© The Society of Theoretical and Applied Mechanics 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Chao, C.K., Wu, C.H., Ting, K. “The Inversion and Kelvin’s Transformation in Plane Thermoelasticity with Circular or Straight Boundaries,” Journal of Mechanics, 34(5), pp.616–627, 2018.CrossRefGoogle Scholar
Kumar, R., Miglani, A., Tani, R., “Generalized Two Temperatures Thermoelasticity of Micropolar Porous Circular Plate with Three Phase Lag Model,” Journal of Mechanics, 34(6), pp.779–789, 2018.CrossRefGoogle Scholar
Kumar, R., Devi, S., “Effects of Phase-Lag on Thick Circular Plate with Heat Sources in Modified Couple Stress Thermoelastic Medium,” Journal of Mechanics, 32(6), pp.665–671, 2016.CrossRefGoogle Scholar
Camp, C.V., Gipson, G.S., Boundary Element Analysis of Nonhomogeneous Biharmonic Phenomena, Springer-Verlag, Berlin, 1992.CrossRefGoogle Scholar
Deb, A., Banerjee, P.K., “BEM for General Anisotropic 2D Elasticity Using Particular Integrals,” Communications in Applied Numerical Methods, 6, pp.111–119, 1990.CrossRefGoogle Scholar
Nardini, D., Brebbia, C.A., “A New Approach to Free Vibration Analysis Using Boundary Elements,” Boundary Element Methods in Engineering, Computational Mechanics Publications, Southampton (1982).Google Scholar
Rizzo, F.J., Shippy, D.J., “An Advanced Boundary Integral Equation Method for Three-Dimensional Thermoelasticity,” International Journal of Numerical Methods in Engineering, 11, pp.1753–1768, 1977.CrossRefGoogle Scholar
Gao, X.W., “Boundary Element Analysis in Thermoelasticity with and without Internal Cells,” International Journal of Numerical Methods in Engineering, 57(7), pp.975–990, 2003.CrossRefGoogle Scholar
Wen, P.H., Alliabadi, M.H., Rooke, D.P., “A New Method for Transformation of Domain Integrals to Boundary Integrals in Boundary Element Method,” Communications in Numerical Methods in Engineering, 14, pp.1055–1065, 1998.Google Scholar
Hematiyan, M.R., “A General Method for Evaluation of 2D and 3D Domain Integrals without Domain Discretization and Its Application in BEM,” Computational Mechanics, 39(4), pp.509–520, 2007.CrossRefGoogle Scholar
Mohammadi, M., Hematiyan, M.R., Aliabadi, M.H., “Boundary Element Analysis of Thermo-Elastic Problems with Non-Uniform Heat Sources,” Journal of Strain Analysis in Engineering, 45(8), pp.605–627, 2010.CrossRefGoogle Scholar
Sladek, V., Sladek, J., “Boundary Integral Equation Method in Thermoelasticity Part III: Uncoupled Thermoelasticity,” Applied Mathematical Modelling, 8, pp.413–418, 1984.CrossRefGoogle Scholar
Sladek, J., Sladek, V., Markechova, I., “Boundary Element Method Analysis of Stationary Thermoelasticity Problems in Non-homogeneous Media,” International Journal of Numerical Methods in Engineering, 30, pp.505–516, 1990.CrossRefGoogle Scholar
Shiah, Y.C., “Analytical Transformation of the Volume Integral for the BEM Treating 3D Anisotropic Elastostatics Involving Body-Force,” Computer Methods in Applied Mechanics and Engineering, 278, pp.404–422, 2014.CrossRefGoogle Scholar
Shiah, Y.C., “Analysis of Thermoelastic Stress Concentration around Oblate Cavities in Three-Dimensional Generally Anisotropic Bodies by the Boundary Element Method,” International Journal of Solids and Structures, 81, pp.350–360, 2016.CrossRefGoogle Scholar
Shiah, Y.C., “Analytical Transformation of the Volume Integral for the BEM Treating 3D Anisotropic Elastostatics Involving Body-Force,” Computer Methods in Applied Mechanics and Engineering, 278, pp.404–422, 2014.CrossRefGoogle Scholar
Shiah, Y.C., Chong, Juin-Yu, “Boundary Element Analysis of Interior Thermoelastic Stresses in Three-Dimensional Generally Anisotropic Bodies,” Journal of Mechanics, 32(6), pp.725–735, 2016.CrossRefGoogle Scholar
Shiah, Y.C., Hsu, Chung-Lei, Hwu, Chyanbin, “Direct Volume-to-Surface Integral Transformation for 2D BEM Analysis of Anisotropic Thermoelasticity,” Computer Modeling in Engineering & Sciences, 102(4), pp.257–270, 2014.Google Scholar
Shiah, Y.C., Tuan, N.A, Hematiyan, M.R., “Direct Transformation of the Volume Integral in the Boundary Integral Equation for Treating Three-Dimensional Steady-State Anisotropic Thermoelasticity Involving Volume Heat Source,” International Journal of Solids and Structures, 143, pp.287–297, 2018.CrossRefGoogle Scholar
Tuan, N.A., Shiah, Y.C., “BEM Study Of 3D Heat Conduction in Multiply Adjoined Anisotropic Media with Quadratic Domain Heat Generation,” Journal of Mechanics, https://doi.org/10.1017/jmech.2018.47, 2019.CrossRefGoogle Scholar
Lifshitz, I.M., Rosenzweig, L.N., “Construction of the Green Tensor for the Fundamental Equation of Elasticity Theory in the Case of Unbounded Elastically Anisotropic Medium,” Zh. Eksp. Teor. Fiz, 17, pp.783–791, 1947.Google Scholar
Ting, T.C.T., Lee, V.G., “The Three-Dimensional Elastostatic Green’s Function for General Anisotropic Linear Elastic Solid,” The Quarterly Journal of Mechanics and Applied Mathematics, 50, pp.407–426, 1997.CrossRefGoogle Scholar