Abstract
Under study is the coefficient inverse problem of thermoelasticity for finite inhomogeneous bodies. We obtain the operator equations of the first kind for the Laplace transform of a solution for solving the nonlinear inverse problem by an iterative process. Solving the inverse problems of thermoelasticity in the originals relies on applying the inverse Laplace transform to these operator equations on using the theorems of operational calculus on the convolution and differentiation of the original. We provide some procedure for reconstructing the thermomechanical characteristics of a rod, a layer, and a cylinder. Finding an initial approximation for the iterative process bases on two approaches. Then an initial approximation is found in the class of bounded positive linear functions, while the coefficients of the functions are determined as minimizers of the residual functional. The other approach to finding an initial approximation bases on algebraization. Numerical experiments were carried out to recover both monotone and nonmonotone functions. Only one characteristic is restored while the others are assumed known. Monotone functions are restored better than nonmonotone ones. While reconstructing the characteristics of stratified materials, the greatest error arises in a neighborhood about the junction points. The reconstruction procedure turned out resistant to noise in the input information.
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Translated from Vladikavkazskii Matematicheskii Zhurnal, 2022, Vol. 24, No. 2, pp. 75–84. https://doi.org/10.46698/v3482-0047-3223-o
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Vatulyan, A.O., Nesterov, S.A. Study of the Inverse Problems of Thermoelasticity for Inhomogeneous Materials. Sib Math J 64, 699–706 (2023). https://doi.org/10.1134/S0037446623030175
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DOI: https://doi.org/10.1134/S0037446623030175
Keywords
- inverse problem of thermoelasticity
- functionally graded materials
- operator equations
- iterative process
- algebraization method