Functionally graded and pre-strained materials find wide application in various engineering fields with large thermo-mechanical loads. Knowing the exact laws heterogeneity of materials after fabrication requires the solution of coefficient inverse problems of thermoelasticity. In this work we present the formulation of the inverse problems of thermoelasticity for pre-stressed functionally graded cylinder. The direct problem is solved on the basis of the method of adjustment in transform by Laplace and use handling procedures implemented in accordance with the method of Durbin. As additional information when solving the inverse problem is the measured displacement at the external border. For the solution of nonlinear inverse problems based on the method of linearization was built by an iterative process. Thermomechanical characteristics were recovered in two stages. The first stage was an initial approximation. In the second stage of the amendment to the restoring characteristics were determined from the solution of the Fredholm integral equations of the 1st kind. The results of computational experiments are presented. The influence of prestressed term on the results of reconstruction of thermoelastic characteristics is considered.

Сформулирована задача об определении неоднородных характеристик предварительно-напряженного функционально-градиентного термоупругого цилиндра. Колебания цилиндра вызываются действием равномерно распределенной нагрузки, приложенной на внешней границе. Разработан итерационный подход к решению поставленной задачи, основанный на применении метода линеаризации. Исследовано влияние начальных напряжений на результаты реконструкции термомеханических характеристик цилиндра.