New Domain Integral Transformation in Boundary Element Analysis for 2D Anisotropic Thermoelasticity
Publication: Journal of Engineering Mechanics
Volume 142, Issue 9
Abstract
As is well known in the boundary element method (BEM), thermal effect reveals itself as an additional volume integral in the associated boundary integral equation. Any attempt to directly integrate it shall require domain discretization that will destroy the BEM’s most distinctive notion of boundary discretization. For anisotropic elastostatics, this additional volume integral can be exactly transformed onto the boundary; however, additional line integrals intersecting the domain are invoked in such a transformation. For simply connected domains, evaluation of the extra line integrals can be avoided by simply employing branch-cut redefinitions; however, the evaluation is inevitable for multiply connected domains. This paper presents a new approach to validate the exact transformation yet without invoking extra line integrals. For the two-dimensional thermoelastic analysis of anisotropic bodies, the present approach has completely restored the BEM’s feature of boundary discretization without extra line integrals involved. In the end, a few typical examples are presented to illustrate the veracity of the formulation and its applicability to engineering practice.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors gratefully acknowledge the financial support from the Ministry of Science and Technology, Taiwan (no. 102-2221-E-006-290-MY3).
References
Cruse, T. A. (1988). Boundary element analysis in computational fracture mechanics, Kluwer Academic Publisher, Dordrecht, Netherlands.
Danson, D. (1983). “Linear isotropic elasticity with body forces, Chap. 4.” Progress in boundary element methods, Vol. 2, C. A. Brebbia, ed., Pentech Press, London.
Deb, A., and Banerjee, P. K. (1990). “BEM for general anisotropic 2D elasticity using particular integrals.” Commun. Appl. Numer. Meth., 6(2), 111–119.
Lekhnitskii, S. G. (1968). Anisotropic plates, Gordon & Breach Science Publisher, New York.
Nardini, D., and Brebbia, C. A. (1982). “A new approach to free vibration analysis using boundary elements.” Boundary element methods in engineering, Computational Mechanics Publications, Southampton.
Nowak, A. J., and Brebbia, C. A. (1989). “A new approach for transforming BEM domain integrals to the boundary.” Eng. Anal. Boundary Elem., 6(3), 164–167.
Rizzo, F. J., and Shippy, D. J. (1977). “An advanced boundary integral equation method for three-dimensional thermoelasticity.” Int. J. Numer. Meth. Eng., 11(11), 1753–1768.
Shiah, Y. C., and Tan, C. L. (1997). “BEM treatment of two-dimensional anisotropic field problems by direct domain mapping.” Eng. Anal. Boundary Elem., 20(4), 347–351.
Shiah, Y. C., and Tan, C. L. (1999). “Exact boundary integral transformation of the thermoelastic domain integral in BEM for general 2D anisotropic elasticity.” Comput. Mech., 23(1), 87–96.
Sladek, J., Sladek, V., and Markechova, I. (1990). “Boundary element method analysis of stationary thermoelasticity problems in non-homogeneous media.” Int. J. Numer. Meth. Eng., 30(3), 505–516.
Sladek, V., and Sladek, J. (1984a). “Boundary integral equation method in thermoelasticity Part III: Uncoupled thermoelasticity.” Appl. Math. Modell., 8(6), 413–418.
Sladek, V., and Sladek, J. (1984b). “Boundary integral equation method in two-dimensional thermoelasticity.” Eng. Anal., 1(3), 135–148.
Information & Authors
Information
Published In
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Dec 1, 2015
Accepted: Apr 7, 2016
Published online: May 20, 2016
Published in print: Sep 1, 2016
Discussion open until: Oct 20, 2016
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.