Abstract
Abstract The bearing elements of power plants, internal combustion engines of jet engines, nuclear thermal power plants, gas-generating power plants, processing lines, and spacecraft antennas are rods of variable cross-section. They work in a difficult temperature environment. In this paper, we propose an algorithm for applying the fundamental law of energy conservation for a deep study of the resulting thermal-stress-strain state of a rod of limited length and variable cross-section in the simultaneous presence of local temperatures, heat exchange and thermal insulation. At the same time, the obtained solutions in the form of determining the temperature field, displacement, all the components of deformations and stresses, as well as the calculated values of the rod elongation and the resulting axial force are highly accurate at the level of satisfying the energy conservation law.