Mathematical and computational modeling of nonlinear steady-state thermo-physical processes in variable cross-section rods

Project type: Grant financing of scientific and (or) research-engineering projects for the Science Committee Ministry of Education and Science of the RK

Code of the project: №AP05131093 (01.01.2018 – 31.12.2020)

Title: Mathematical and computational modeling of nonlinear steady-state thermo-physical processes in variable cross-section rods.

The object of research, development or design: The thermo-physical state of the rod is investigated taking into account the existing non-linear dependencies and boundary conditions, the cross section of which can be in the form of various geometric shapes.

Aim of work: The project purpose is to develop mathematical and computational modeling of nonlinear steady-state thermo-physical processes in the variable cross-section rods. Bearing elements of the modern power units operate under the simultaneous influence of diverse types of heat sources. In this regard, they are made of the special variable cross-section rods.

Research methods: For modeling the steady-state nonlinear thermo-physical processes in the structural elements made of the variable cross-section rods operating under the influence of diverse types of heat sources used, the fundamental law of energy conservation is used. Herewith the temperature dependence of the thermal expansion coefficients and elastic modulus of materials are considered for different operating conditions. For building the systems of linear algebraic equations based on the fundamental law of energy conservation, the studied structural element of the variable cross-section rods is discretized. Further, minimizing this functional by a discrete temperature values, the resolving system of linear algebraic equations is built. In these equations natural operating conditions will be considered. Solving this system the temperature value in the discrete points of the structural element of the variable cross-section rods is determined. Next, using the built spline-functions, a temperature distributing field is defined. Then, using the relevant dependences of the coefficients of thermal expansion and modulus of the material elasticity, the field distributing their valuesis determined. Solving the system, the values of the rod displacements at discrete points are determined. Using the built spline-functions, the displacement field of all components of strains and stress arising in the structural elements made of the variable cross-section rods is determined. In addition, this article investigates the convergence, stability and accuracy of the proposed methods.

Field of application:  Results of a research will be applied to ensure the smooth continuous operation of strategic facilities, where it is required to calculate the arising non-linear thermo-physical phenomena and their influence on the bearing structural elements in the form of the variable cross-section rods. These facilities include nuclear power plants, gas plants, and thermal power plants used in business purposes, where a large volume of electricity is produced when exposed to heterogeneous heat sources and need reliability.

Project Investigator: Kudaykulov A. (IICT CS MES RK)

The organization – executor: IICT CS MES RK