Some problems of identification of physical and mechanical characteristics of inhomogeneous bodies under thermal loading

Authors

  • Nesterov S.A. Southern Mathematical Institute, a branch of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Russian Federation ORCID iD 0000-0003-3780-5104

UDC

539.3, 563.24

EDN

HVZNRK

DOI:

10.31429/vestnik-22-3-13-23

Abstract

Research in the field of inverse problems of identification of variable physical and mechanical characteristics is very relevant due to the widespread use of functionally graded materials in engineering. However, the technological process of their manufacture, due to its multi-stage nature, does not allow to accurately predicting the properties of the finished product. A class of coefficient inverse problems is considered in which the reconstruction of variable physical and mechanical characteristics of bodies under the action of thermal stationary loads is carried out using information on the temperature and displacement fields measured on the part of the boundary free from loading. As examples, the problems of identification of one-dimensional characteristics are studied: 1) the thermal conductivity coefficient of a rod; 2) the compliance coefficient of a thermoelastic rod; 3) the thermal conductivity coefficient of an elongated rectangle. The solution to the first problem is constructed by approximating the derivative of the temperature on the segment of additional information removal using the Galerkin projection method and extending the definition of the derivative quadratically in the remaining part of the rod. The solutions of the second and third problems are based on the algebraization of physical fields and narrowing the search class to polynomial functions whose coefficients are found from the solution of linear algebraic systems. The results of computational experiments on the reconstruction of variable physical and mechanical characteristics of a rod and an elongated rectangle are presented. It is found that narrowing the search area significantly increases the efficiency of the proposed approaches in restoring functions from the same class.

Keywords:

rod, rectangle, functionally graded materials, thermal conductivity coefficient, Young's modulus, compliance coefficient, coefficient inverse problem, identification, Galerkin method, weak statement

Funding information

The study did not have sponsorship.

Author info

  • Sergey A. Nesterov

    д-р физ.-мат. наук, ведущий научный сотрудник отдела дифференциальных уравнений Южного математического института – филиала ВНЦ РАН

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Issue

Vol. 22 (2025) No. 3

Pages

13-23

Section

Mechanics

Dates

Submitted

July 14, 2025

Accepted

September 8, 2025

Published

September 22, 2025

How to Cite

[1]
Nesterov, S.A., Some problems of identification of physical and mechanical characteristics of inhomogeneous bodies under thermal loading. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2025, т. 22, № 3, pp. 13–23. DOI: 10.31429/vestnik-22-3-13-23

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