Algorithm of solving of nonstationary thermoelastic problem for two-layered cylinder at time-variety heat transfer coefficient


  • O. G. Kutsenko Taras Shevchenko National University of Kyiv
  • O. M. Kharytonov Taras Shevchenko National University of Kyiv



nonstationary thermoelasticity, two-layer cylinder, thermal shock


The nonstationary axisymmetric thermoelasticity problem for a two-layer cylinder at the inner surface of which convective heat transfer with an environment takes place is considered. The solution of this problem is derived for the case of inhomogeneous initial temperature field. The solution is presented in the form of development by the system of eigenfunctions of the boundary value problem for a two-component beam and expressed in terms of the elementary functions. Based on this solution, an incremental algorithm of solving thermoelasticity problems for a two-layer cylinder is proposed for the case that the heat transfer coefficient between the inner surface of the cylinder and environment is time-varied. The idea of the algorithm is to divide the entire transient time interval into a sequence of subintervals, the heat transfer coefficient is considered constant on each. Once the temperature field is determined, the axisymmetric stress field can be founded on the basis of analytical expressions. The proposed algorithm was tested on the example of the thermal shock scenario for a nuclear reactor vessel. The comparison of the obtained results with the numerical solution by the finite element method verified sufficient working accuracy of the proposed approach.

Pages of the article in the issue: 59 - 62

Language of the article: Ukrainian


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(2020) A Free Software Three-Dimensional Structural Finite Element Program. Available from:




How to Cite

Kutsenko, O. G., & Kharytonov, O. M. (2021). Algorithm of solving of nonstationary thermoelastic problem for two-layered cylinder at time-variety heat transfer coefficient. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (3), 59–62.



Differential equations, mathematical physics and mechanics