### APPLICATION OF THE METHOD OF BOUNDARY INTEGRAL EQUATIONS FOR NON-STATIONARY PROBLEM OF THERMAL CONDUCTIVITY IN AXIALLY SYMMETRIC DOMAIN

#### Abstract

The** **article considers the non-stationary initial-boundary problem of thermal conductivity in axially symmetric domain in Minkowski space, formulated as equivalent boundary integral equation. Using the representation of the solution in the form of a Fourier series expansion, the problem is reformulated as an infinite system of two-dimensional singular integral equations regarding expansion coefficients. The paper presents and investigates the explicit form for fundamental solutions used in the integral representation of the solution in the domain and on the border. The obtained results can be used in the construction of efficient numerical boundary element method for estimation of structures behavior under the influence of intense thermal loads in real-time.

#### Keywords

#### Full Text:

PDF#### References

Kartashov, E., Kudinov, V. (2012). Analytical theory of heat conduction and thermoelasticity. Librocom, 656.

Lurie, A. I. (2010). Theory of Elasticity. Springer Science & Business Media, 1050. doi: 10.1007/978-3-540-26455-2

Maceri, A. (2010). Theory of Elasticity, 1st Edition. Springer Science & Business Media, 716. doi: 10.1007/978-3-642-11392-5

Zarubin, V., Kyvurkin, G. (2002). Mathematical models of thermal mechanics. Moscow: Fizmatlit, 168.

Wrobel, L. C., Aliabadi, M. H. (2002). The Boundary Element Method, New York: John Wiley & Sons, 1066.

Constanda, C., Doty, D., Hamill, W. (2016). Boundary Integral Equation Methods and Numerical Solutions. New York: Springer, 232. doi: 10.1007/978-3-319-26309-0

Schanz, M., Steinbach, O. (2007). Boundary Element Analysis – Mathematical Aspects and Applications. Lecture Notes in Applied and Computational Mechanics, 352. doi: 10.1007/978-3-540-47533-0

Zrazhevsky, G., Zrazhevska, V. (2016). Obtaining and investigation of the integral representation of solution and boundary integral equation for the non-stationary problem of thermal conductivity. Eureka: Physics and Engineering, 6, 53–58. doi: 10.21303/2461-4262.2016.00216

Reddy, J. N. (2006). An Introduction to the Finite Element Method, 3rd Edition. McGraw Hill, 672.

Chaskalovic, J. (2008). Finite Elements Methods for Engineering Sciences. Springer Verlag, 267.

DOI: http://dx.doi.org/10.21303/2461-4262.2017.00285

### Refbacks

- There are currently no refbacks.

Copyright (c) 2017 Grigoriy Zrazhevsky, Vera Zrazhevska

This work is licensed under a Creative Commons Attribution 4.0 International License.

ISSN 2461-4262 (Online), ISSN 2461-4254 (Print)