Abstract
We consider an inverse problem on the identification of two thermomechanical characteristics of a functionally graded pipe based on the additional data picked on the outer surface of the pipe over a finite time interval. The pipe’s thermomechanical characteristics depend on the radial coordinate. Two direct thermoelasticity problems for different thermal loads on the pipe’s outer surface, after applying the Laplace transform, are solved with the help of the shooting method and transform inversion based on the expansion of the actual space in terms of shifted Legendre polynomials. The numerical solution of the inverse problem is built via the iterative process of solving the system of the Fredholm integral equations of the 1st kind. Computational experiments are carried out to restore two thermomechanical characteristics with the known others. It is revealed that monotonic functions are restored with sufficient accuracy; the reconstruction procedure is resistant to 2% input data noise.
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This work was supported by the Southern Mathematical Institute of Vladikavkaz Scientific Center of the Russian Academy of Sciences.
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Nedin, R.D., Nesterov, S.A., Vatulyan, A.O. (2023). Concerning Identification of Two Thermomechanical Characteristics of Functionally Graded Pipe. In: Altenbach, H., Mkhitaryan, S.M., Hakobyan, V., Sahakyan, A.V. (eds) Solid Mechanics, Theory of Elasticity and Creep. Advanced Structured Materials, vol 185. Springer, Cham. https://doi.org/10.1007/978-3-031-18564-9_18
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