Cylindrical vessel with liquid in 3D temperature pattern

N. G. Gur'yanov, O. N. Tyuleneva

Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia

Abstract: We obtain an exact solution of three-dimension thermoelasticity problem for a vessel with liquid in cylindrical coordinate system. Temperature pattern is defined based on a solution of thermal conductivity equation. Next, equations of unsymmetrical problem of the theory of elasticity are solved, besides, the system of resolving equations is reduced to four separate equations relatively to construction displacement. Several exact solutions of boundary-value problems are framed. The results are represented in the form of quite simple formulas.

Keywords: temperature pattern, thermoelasticity, integrable combinations, boundary-value problems, analytical solutions.

UDC: 517.958:519.3

Received: 08.11.2016

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2018, 62:2, 19–27

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