Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-10T14:46:18.825Z Has data issue: false hasContentIssue false
  • English
  • Français

Boundary Element Analysis of Interior Thermoelastic Stresses in Three-Dimensional Generally Anisotropic Bodies

Published online by Cambridge University Press:  16 May 2016

Y.-C. Shiah  and
J.-Y. Chong
Y.-C. Shiah*
Affiliation:
Department of Aeronautics and Astronautics National Cheng Kung University Tainan, Taiwan
J.-Y. Chong
Affiliation:
Department of Aeronautics and Astronautics National Cheng Kung University Tainan, Taiwan
*
*Corresponding author (ycshiah@mail.ncku.edu.tw)
Get access

Abstract

This paper is to present the treatment of internal thermoelastic stress analysis in 3D anisotropic bodies by the boundary element method (BEM). Fundamentally, thermal effects will give rise to an additional volume integral in the boundary integral equation (BIE). By applying the fundamental solutions represented by Fourier series, the volume integral has been analytically transformed to the boundary. For the present work, spatial differentiations of the integral equation are performed to give displacement gradients at internal points of interest. This differentiated integral equation is further implemented to perform thermoelastic stress analysis inside 3D anisotropic bodies. This analysis is particularly important in engineering applications when thermoelastic stresses concentrations are present inside the bodies. The present work is the first BEM implementation for this study by the transformed BIE. In the end, two benchmark examples are tested to demonstrate the applicability of the present BEM treatment.

Keywords

Boundary element methodInternal thermoelastic stresses3D fundamental solutions of anisotropic elasticity
Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 6 , December 2016 , pp. 725 - 735
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2016 

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

1. Rizzo, F. J. and Shippy, D. J., “An Advanced Boundary Integral Equation Method for Three-Dimensional Thermoelasticity,” International Journal for Methods in Engineering, 11, pp. 1753–1768 (1977).Google Scholar
2. Sladek, V. and Sladek, J., “Boundary Integral Equation Method in Thermoelasticity. Part I: General Analysis,” Applied Mathematical Modelling, 7, pp. 241–253 (1984).Google Scholar
3. Shiah, Y. C. and Tan, C. L., “Exact Boundary Integral Transformation of the Thermoelastic Domain Integral in BEM for General 2D Anisotropic Elasticity,” Applied Mathematical Modelling, 7, pp. 241–253 (1984).Google Scholar
4. Park, K. H. and Banerjee, P. K., “Two- and Three-Dimensional Transient Thermoelastic Analysis by BEM via Particular Integrals,” International Journal of Solids and Structures, 39, pp. 2871–2892 (2002).Google Scholar
5. Gao, X. W., “Boundary Element Analysis in Thermoelasticity with and without Internal Cells,” International Journal for Methods in Engineering, 57, pp. 957–990 (2003).Google Scholar
6. Suh, I. G. and Tosaka, N., “Application of the Boundary Element Method to 3-D Linear Coupled Thermoelasticity Problems,” Theoretical and Applied Mechanics, 38, pp. 169–175 (1989).Google Scholar
7. Dargush, G. F. and Banerjee, P. K., “Application of the Boundary Element Method to 3-D Linear Coupled Thermoelasticity Problems,” Theoretical and Applied Mechanics, 38, pp. 169–175 (1989).Google Scholar
8. Tosaka, N. and Suh, I. G., “Boundary Element Analysis of Dynamic Coupled Thermo-Elasticity Problems,” Computational Mechanics, 8, pp. 331–342 (1991).Google Scholar
9. Chen, J. and Dargush, G. F., “Boundary Element Method for Dynamic Poroelastic and Thermoelastic Analyses,” International Journal of Solids and Structures, 32, pp. 2257–2278 (1995).Google Scholar
10. Hosseini-Tehrani, P. and Eslami, M. R., “BEM Analysis of Thermal and Mechanical Shock in a Two-Dimensional Finite Domain Considering Coupled Thermoelasticity,” Engineering Analysis with Boundary Elements, 24, pp. 249–257 (2000).Google Scholar
11. Shiah, Y. C., Hematiyan, M. R. and Chen, Y. H., “Regularization of the Boundary Integrals in the BEM Analysis of 3D Potential Problems,” Journal of Mechanics, 29, pp. 385–401 (2013).Google Scholar
12. Shiah, Y. C., “3D Elastostatic Boundary Element Analysis of Thin Bodies by Integral Regularizations,” Journal of Mechanics, 31, pp. 533–543 (2014).Google Scholar
13. Gao, X.-W., Zhenga, B.-J., Yanga, K. and Zhang, Ch., “Radial Integration BEM for Dynamic Coupled Thermoelastic Analysis Under Thermal Shock Loading,” Computers & Structures, 158, pp. 140–147 (2015).Google Scholar
14. Shiah, Y. C. and Tan, C. L., “The Boundary Integral Equation for 3D General Anisotropic Thermoelasticity,” Computer Modelling Engineering Science, 102, pp. 425–447 (2014).Google Scholar
15. 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).Google Scholar
16. Tan, C. L., Shiah, Y. C. and Wang, C. Y., “Boundary Element Elastic Stress Analysis of 3D Generally Anisotropic Solids Using Fundamental Solutions Based on Fourier Series,” International Journal of Solids and Structures, 50, pp. 2701–2711 (2013).Google Scholar
17. Deb, A. and Banerjee, P. K., “BEM for General Anisotropic 2D Elasticity Using Particular Integrals,” Communications in Numerical Methods in Engineering, 6, pp. 111–119 (1990).Google Scholar
18. Nardini, D. and Brebbia, C. A., “A New Approach to Free Vibration Analysis Using Boundary Elements,” Engineering Analysis with Boundary Elements, 7, pp. 157–162 (1983).Google Scholar
19. Ting, T. C. T. and Lee, V. G., “The Three-Dimensional Elastostic Green's Function for General Anisotropic Linear Elastic Solid,” Quarterly Journal of Mechanics and Applied Mathematics, 50, pp. 407–426 (1997).Google Scholar
20. Shiah, Y. C. and Tan, C. L., “Exact Boundary Integral Transformation of the Thermoelastic Domain Integral in BEM for General 2D Anisotropic Elasticity,” Computational Mechanics, 23, pp. 87–96 (1999).CrossRefGoogle Scholar
21. Huntington, H. B., The Elastic Constants of Crystals, Academic Press, New York (1958).Google Scholar