MATHEMATICAL MODELING AND DEVELOPMENT OF A COMPUTATIONAL ALGORITHM FOR INVESTIGATING THE THERMALLY STRESSED STATE OF A HEAT-RESISTANT ALLOY

Abstract

Many basic load-bearing structural elements operating in a large thermal field (el-
ements of gas turbine and jet engines, etc.), in the presence of external forces, are made of heat-
resistant alloys. The physical feature of such alloys is that the coefficient of thermal expansion and
the modulus of elasticity of the material strictlydependsonthetemperaturedistributionfield, thatis,
thecoefficientsare a functionoftemperature.
In this work, on the basis of the law of conservation of energy, the thermally stressed state in
the rod elements of the structure is modeled, in the presence of a heat flux supplied on the lateral
surface, which varies along the coordinate in a linear manner.
To solve the problem under consideration, a potential energy minimization method is used in
combination of a quadratic finite element with three nodes. From the condition of the minimum of
the functional characterizing the potential energy, a resolving system of linear algebraic equations is
obtained. All possible natural boundary conditions are taken into account here. In this system, all integrals used are calculated analytically. Moreover, the law of conservation of energy is fulfilled
for each of the equations of the resulting system.
The values of displacement, deformation and stresses, as well as the values of elastic tempera-
ture and thermoelastic components of deformations and stresses are calculated for a specific exam-
ple.