# Solution of the axisymmetric problem of thermoelasticity of a radially inhomogeneous cylindrical shell by numerical-analytical method and the finite element method

## Abstract

The aim of research is to compare two calculation methods using the example of solving the axisymmetric thermoelasticity problem. Methods. The calculation of a thick-walled cylindrical shell on the temperature effect was carried out by the numerical-analytical method and the finite element method, implemented in the LIRA-CAD software package. The shell consists of three layers: two layers of heat-resistant concrete and an outer steel layer. In the calculation, a piecewise linear inhomogeneity of the shell due to its three-layer structure and continuous inhomogeneity caused by the influence of a stationary temperature field is taken into account. The numerical-analytical method of calculation involves the derivation of a resolving differential equation, which is solved by the sweep method, it is possible to take into account the nonlinear nature of the deformation of the material using the method of successive approximations. To solve this problem by the finite element method, a similar computational model of the shell was constructed in the LIRA-CAD software package. The solution of the problem of thermoelasticity for an infinite cylinder (under conditions of a plane deformed state) and for a cylinder of finite length with free ends is given. Results . Comparison of the calculation results is carried out according to the obtained values of ring stresses σθ.

## About the authors

### Lyudmila S. Polyakova

Moscow State University of Civil Engineering (National Research University)

Author for correspondence.
Email: asv@mgsu.ru
SPIN-code: 4913-4377

master, graduate student, Department of Strength of Materials

26 Yaroslavskoye shosse, Moscow, 129337, Russian Federation

### Vladimir I. Andreev

Moscow State University of Civil Engineering (National Research University)

Email: asv@mgsu.ru
SPIN-code: 9906-7214

Doctor of Technical Sciences, Professor, Head of the Department of Strength of Materials

26 Yaroslavskoye shosse, Moscow, 129337, Russian Federation

## References

1. Andreev V.I., Polyakova L.S. (2016). Physically nonlinear problems for inhomogeneous thick-walled shells. International Journal for Computational Civil and Structural Engineering, 12(4), 36–40. (In Russ.)
2. Ushakov A.V. (2006). Osnovnye zakonomernosti deformirovaniya obychnogo i zharostojkih betonov pri nagreve [The basic laws of deformation of conventional and heat-resistant concrete during heating]. (PhD dissertation, Volgograd). 212. (In Russ.)
3. Lucas P.A. (1978). Osnovy nelineinoi stroitel'noi mekhaniki [The foundations of nonlinear structural mechanics]. Moscow: Stroizdat Publ., 208. (In Russ.)
4. Polyakova L.S., Andreev V.I. (2018). Calculation of a nonlinearly elastic three-layer cylindrical shell taking into account the continuous inhomogeneity caused by the temperature field. IOP Conf. Series: Materials Science and Engineering, 456, 012124.
5. SP 27.13330.2011. (2011). Betonnye i zhelezobetonnye konstrukcii, prednaznachennye dlya raboty v usloviyah vozdejstviya povyshennyh i vysokih temperatur [Concrete and reinforced concrete structures designed to work in conditions of exposure to high and high temperatures]. Moscow, 116. (In Russ.)
6. Andreev V.I., Polyakova L.S. (2019). Calculation of nonlinear elastic three-layer cylindrical shell of finite length with taking into account the continuous inhomogeneity caused by the temperature field. E3S Web of Conferences, 91, 02018.

Copyright (c) 2019 Polyakova L.S., Andreev V.I.

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

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