Using the Method of Finite Differences to Solve the Rod Fuel Element Shell Stress-Strain Behavior Problem
DOI:
https://doi.org/10.20998/2078-774X.2017.09.13Анотація
The stress-strain behavior definition is required to simulate the behavior of the shell of a fuel element and it requires the solution of appropriately formulated problem on the mechanics of strained solid body taking into consideration the geometric shape, fastening conditions, external influence factors and material characteristics. The purpose of this scientific paper was to study the opportunities of the method of finite differences to solve the problem on the definition of the stress-strain behavior of the shells of fuel elements used by nuclear reactors. Stress-strain behavior of the shell is viewed within the bounds of known hypothesis of axisymmetric plane deformation. Consideration is given to different mathematical formulations of the problem on the stress-strain behavior of the shell of fuel element. It has been shown that the most promising formulation is the one with independent unknown stresses and displacements, because it has no derivatives of temperature relationships for material characteristics. The method of finite differences is rather promising for the solution of problems solved to define the stress-strain behavior of the shells of fuel elements. Though the method of finite differences is believed to be well-studied, however the use of this method for differential equations that satisfy the mathematical formulation with independent unknown stresses and displacements requires additional studies and it should be noted that particularly such formulations are of great interest.Посилання
Imani, M., Aghaie, M., Zolfaghari, A. and Minuchehr, A. (2015), "Numerical study of fuel–cladmechanicalinteractionduringlong-term burnup of WWER1000", Annals of Nuclear Energy, Vol. 80. pp. 267–278, ISSN 0306-4549,doi:10.1016/j.anucene.2015.01.036.
Tulkki, V. and Ikonen, T. (2015), "Modelling anelastic contribution to nuclear fuel cladding creep and stress relaxation",Journalof Nuclear Materials, Vol. 465, pp. 34–41, ISSN 0022-3115, doi: 10.1016/j.jnucmat.2015.04.056.
Suzuki, M. (2000), Light water reactor fuel analysis code FEMAXI-V (VER. 1), Japan atomic energy research institute.
Maceri, A. (2010), Theory of Elasticity, Springer-Verlag Berlin Heidelberg, ISBN 978-3-642-11392-5.
Barber, J. R. (2010), Elasticity, Springer, Netherlands, ISBN 978-90-481-3809-8.
Anandarajah, A. (2010), Computational Methods in Elasticity and Plasticity, Springer-Verlag, New York, ISBN 978-1-4419-6379-6.
Morachkovskii, O. K. and Romashov, Yu. V. (2009), "Solving initial-boundary-value creep problems", InternationalAppliedMechanics, Vol. 45, No. 10, pp. 1061–1070.
Morachkovskii, O. K. and Romashov, Yu. V. (2011), "Prediction of the corrosion cracking of structures under the conditionsofhigh-temperature creep", Materials Science, Vol. 46, No. 5, pp. 613–618, ISSN 1068-820X, doi: 10.1007/s11003-011-9331-7.
Fletcher, C. A. J. (1988, 1991), Computational techniques for fluid dynamics 1 Fundamental and General Techniques,SpringerVerlag, Berlin, Heidelberg.
