# Numerical modeling of thermoelasticity problems for constructions with inner heat source

• Vasilyeva Maria V., vasilyevadotmdotv@gmail.com M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 42 Kulakovsky Street, Yakutsk 677000, Russia
• Zakharov Petr E., zapetch@gmail.com M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 42 Kulakovsky Street, Yakutsk 677000, Russia
• Sivtsev Petr V., sivkapetr@mail.ru M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 42 Kulakovsky Street, Yakutsk 677000, Russia
• Spiridonov Denis A., d.stalnov@mail.ru M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 42 Kulakovsky Street, Yakutsk 677000, Russia
Keywords: thermoelasticity problems, thermal expansion, heat transfer, linear elasticity problem, plasticity models, nonlinear problems, ﬁnite element method, mathematical modeling

### Abstract

We consider the numerical simulation of the thermomechanical state of a structure consisting of a heat source, a gas gap and a shell. The mathematical model is described by a nonlinear system of equations for temperature and displacements. The heat is released in the subdomain of the heat source. The resulting displacements due to the temperature gradient are calculated in the heat source region and separately in the shell, and can be described by both linear elasticity models and nonlinear plasticity models. The numerical implementation is based on the ﬁnite element method. The results of numerical modeling of a nonlinear model problem in two- and three-dimensional domains are presented.

### References

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How to Cite
Vasilyeva, M., Zakharov, P., Sivtsev, P. and Spiridonov, D. (&nbsp;) “Numerical modeling of thermoelasticity problems for constructions with inner heat source”, Mathematical notes of NEFU, 24(3), pp. 52-64. doi: https://doi.org/10.25587/SVFU.2018.3.10889.
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Mathematical Modeling