СОВРЕМЕННЫЕ ОБЛАСТИ ПРИЛОЖЕНИЯ ОБРАТНЫХ ЗАДАЧ МАТЕМАТИКИ И ФИЗИКИ

Abstract

In this article the questions of modern mathematical design of different processes (computer tomography, non-destructive control, and, exactly, ultrasonic fault detection of and other) come into question from the point of view of theory of reverse tasks. Besides, the article proposes an approach to determining the maximum thermal load measured with a certain error of temperature (thermal) stress by solving the inverse problem of thermal elasticity. To obtain a stable solution of the inverse problem of thermoelasticity, the A.N. Tikhonov method with effective search for the regularization parameter is used. The A.N. Tikhonov functional reflects the deviation of the temperature stress obtained as a result of the observation from the finite element method calculated on the basis of the approximate solution of the direct elasticity problem. Examples of reverse tasks are made, their basic features and prospects of the use are discussed in a design.. Experimentally is theoretical research of thermoelastic descriptions of materials of devices, and also elements of турбостроения comes true coming from the decision of reverse problems of thermoelasticity. Greate importance in solving inverse problems are the issues of measurement uncertainty, which affects the final results.