Numerical realization of the iterative scheme for solving inverse thermoelasticity problems for inhomogeneous bodies with coatings
Bodies with coatings are a widespread class of modern materials. In this paper, we consider a dynamic problem for an inhomogeneous thermoelastic layer with a functional gradient covering. Functions characterizing the inhomogeneity have breakpoints of the first kind at the interface of the coating with the substrate. The solution scheme is based on the preliminary reduction of the problem by means of the Fourier transform to two simpler one-dimensional unrelated problems with respect to the averaged characteristics. The inverse problem consists in determining the thermomechanical characteristics that allows the existence of a discontinuity point of the first kind at the boundary physical fields. After applying the Laplace transform the direct problem of thermoelasticity is solved on the basis of the method of reduction to the system of integral Fredholm equations of the second kind and the inversion of solutions on the basis of the theory of residues. To solve the inverse problem, an iterative process is constructed, at each stage of which there are corrections of the reconstructed characteristics by solving the Fredholm integral equation of the first kind. During the computational experiments, analysis of the effect of the coating stiffness was performed. The relative thickness of the coating on the results of reconstruction of inhomogeneous thermomechanical characteristics was investigated. Practical recommendations on the selection of the most informative time intervals for measuring the input information are given.