Computer simulation of the plane thermoelasticity problems: comparative analysis of coupled and uncoupled statements
DOI:
https://doi.org/10.7242/1999-6691/2017.10.4.30Keywords:
thermoelasticity problem, coupled and uncoupled statements, finite element methodAbstract
A computer simulation of a plane problem of linear thermoelasticity was carried out in coupled and uncoupled statements for an inhomogeneous medium with a hole. In the case of uncoupled statement at first we solve an independent part of the thermoelasticity problem, the nonstationary heat conduction equation without taking into account the term responsible for the mechanical power of internal forces with the Dirichlet boundary conditions, and determine the distribution of temperature. Then we proceed to the static problem of thermoelastic stresses based on the equilibrium equations and the Duhamel-Neumann law with the Neumann boundary condition and a given temperature distribution. For the discretization of differential equations, we use the finite element method which is based on the construction of a vector-matrix system of equations formed on the weak form of thermomechanical equations under the condition of quasistatic deformation. The finite element method is implemented in the specially designed home-made code PIONER. As a test problem, we considered a problem of cooling a hollow cylinder with prescribed temperatures and stresses on the inner and outer surfaces. The problem was solved using eight-node finite elements with a reduced biquadratic approximation of geometry and displacements within a plane strain model. Numerical experiments have shown that under certain restrictions that simplify the problem: the absence of mass forces, initial stresses, heat sources and convection on a part of the surface, for the given class of problems, the distribution of displacements, stresses, and temperature in coupled problems is close to that in uncoupled formulation. The obtained results are consistent with the fact that in the linear thermoelasticity the term in the heat conduction equation, responsible for the mechanical power of internal forces, has no significant effect on the solution of the thermoelastic system.
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References
Novackij V. Dinamiceskie zadaci termouprugosti. - M.: Mir, 1970. - 256 s.
2. Ranc N., Palin-Luc T., Paris P.C. Thermal effect of plastic dissipation at the crack tip on the stress intensity factor under cyclic loading // Eng. Fract. Mech. - 2011. - Vol. 78, no. 6. - P. 961-972.
3. Ouzia A., Antonakakis T. Uncoupled thermoelasticity solutions applied on beam dumps // Phys. Rev. Accel. Beams. - 2016. - Vol. 19. - 063501.
4. Kovalenko A.F. Rezimy vysokotemperaturnogo lazernogo otziga opticeskoj keramiki KO-3 izluceniem SO2-lazera // Steklo i keramika. - 2015. - No 11. - S. 17-21.
5. Kleiber M., Kowalczyk P. Introduction to nonlinear thermomechanics of solid / Lecture Notes on Numerical Methods in Engineering and Sciences. - Springer, 2016. - 345 p.
6. Rogovoj A.A. Termouprugoplasticeskie processy s konecnymi deformaciami // Vycisl. meh. splos. sred. - 2013. - T. 6, No 3. - S. 373-383.
7. Carter J.P., Booker J.R. Finite element analysis of coupled thermoelasticity // Comput. Struct. - 1989. - Vol. 31, no. 1. - P. 73-80.
8. Carter J.P. AFENA - A Finite Element Numerical Algorithm - Users’ Manual. - School of Civil and Mining Engineering, University of Sydney, Australia, 1986.
9. Zhihui Li, Qiang Ma, Junzhi Cui. Finite element algorithm for dynamic thermoelasticity coupling problems and application to transient response of structure with strong aerothermodynamic environment // Commun. Comput. Phys. - 2016. - Vol. 20, no. 3. - P. 773-810.
10. Kovalenko A.D. Osnovy termouprugosti. - Kiev: Nauk. dumka, 1970. - 309 s.
11. Eringen A.C. Mechanics of continua. - New York: Huntington, 1980. - 592 p.
12. Agalovan L.A., Gevorkan R.S., Sarkisan A.G. Sravnitel’nyj asimptoticeskij analiz nesvazannoj i svazannoj teorij termouprugosti // MTT. - 2014. - No 4. - P. 38-53.
13. Lycev S.A., Manzirov A.V., Uber S.V. Zamknutye resenia kraevyh zadac svazannoj termouprugosti // MTT. - 2010. - No 4. - S. 138-154.
14. Korobeinikov S.N., Agapov V.P., Bondarenko M.I., Soldatkin A.N. The general purpose nonlinear finite element structural analysis program PIONER // Proc. Int. Conf. Num. Meth. Appl. - Sofia: Publ. House Bulgarian Acad. Sci., 1989. - P. 228-233.
15. Polivka R.M, Wilson E.L. Finite element analysis of nonlinear heat transfer problems. - Berkeley: University of California, 1976.
16. Kreith F. Principles of heat transfer. - New York: Intext Press Inc., 1973. - 414 p.
17. Timosenko S.P., Gud’er Dz. Teoria uprugosti. - M.: Nauka, 1975. - 576 c.
18. Bathe K.J. Finite element procedures. - Prentice Hall, New Jersey, Upper Saddle River, 1996. - 1037 p.
19. Curnier A. Computational methods in solid mechanics. - Kluwer Academic Publ., Dordrecht, 1994. - 404 p.
20. Hughes T.J.R. The finite element method: linear static and dynamic finite element analysis. - Hall, Englewood Cliffs, 1987. - 803 p.
21. Korobejnikov S.N. Nelinejnoe deformirovanie tverdyh tel. - Novosibirsk: Izdatel’stvo SO RAN, 2000. - 262 s.
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