Abstract: The formulation of the coefficient inverse problem of thermoelasticity for finite inhomogeneous bodies is given. Operator equations of the first kind in Laplace transforms are obtained to solve a nonlinear inverse problem on the basis of an iterative process. The solution of inverse problems of thermoelasticity in the originals is based on the inversion of operator relations in transformants using theorems of operational calculus on the convolution and differentiation of the original. The procedure for reconstruction of thermomechanical characteristics of a rod, layer, cylinder is considered. The initial approximation for the iterative process is found on the basis of two approaches. In the first approach, the initial approximation is found in the class of positive bounded linear functions. The coefficients of linear functions are determined from the condition of minimizing the residual functional. The second approach to finding the initial approximation is based on the method of algebraization. Computational experiments were carried out to recover both monotone and non-monotonic functions. One characteristic was restored while the others were known. Monotonic functions are restored better than non-monotonic ones. In the case of reconstructing the characteristics of layered materials, the greatest error occurred in the vicinity of the points of conjugate. The reconstruction procedure turned out to be resistant to noise in the input information.

Keywords: inverse problem of thermoelasticity, functionally graded materials, operator equations, iterative process, algebraization method.

For citation: Vatulyan, À. Î. and Nesterov, S. À. Study of Inverse Problem of Thermoelasticity for Inhomogeneous Materials,
Vladikavkaz Math. J., 2022, vol. 24, no. 2, pp. 75-84 (in Russian). DOI 10.46698/v3482-0047-3223-o

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