Numerical modeling of thermomechanical processes in heat-resistant alloys

Abstract

This article presents a numerical simulation of thermomechanical processes in heat-resistant alloys. The authors develop the law of temperature distribution along the length of the physical body, which is considered as a rod of alloy EI-617. The authors also investigated the dependence of the magnitude of the elongation of the rod from a given temperature. To do this, the rod is conditionally divided into several elements, and then the study is carried out in one area. To determine the temperature dependence, the temperature distribution field is approximated by a full polynomial of the second degree, and approximation spline functions are introduced. Using a temperature gradient for one element, the functional expression characterizing the total thermal energy is written, first for the (n-1) element, then for the last n-th element. The total thermal energy is expressed by the formula    n i i JJ 1 . By minimizing the total thermal energy, we obtain a system of algebraic equations for determining the nodal values of temperatures. Applying the obtained values, the elongation of the element due to thermal expansion is calculated. The relationship between the temperature T, elongation T l , «tensile» force R , and «tensile stress» . is shown in the work. It is shown that with increasing temperature, the above values proportionally increase

Finite element modeling of heat propagation of a complete rod of constant cross-section

“…In this case, the values of the heat transfer coefficient denote by h, and the values of the ambient temperature denote by 𝑇 𝑎𝑡 (Fig. 1) [1,[7][8][9][10][11].…”

“…It is known from the general course of thermophysics that the established process of heat distribution in one-dimensional structural elements is described by the differential equation of the quasi-harmonic form of the parabolic type [1]:…”

“…It is known from the course of calculus of variations that the solution of equation (1), which satisfies boundary conditions (2) and (3) gives a minimum of the following functional: Then if we find a function ) (x T T = , which will give a minimum to the functional (4), then it is a solution of equation (1) and will simultaneously satisfy boundary conditions (2)…”

“…Then the functional expression for the first finite element is as follows [1,2,[12][13][14][15][16]:…”

“…Assume that the considered rod is homogeneous and of constant cross-section. Then for the numerical solution we assume the following initial data [1,2,[17][18][19][20][21][22]: Based on the initial data we have:…”