Abstract
The work is devoted to the use of mathematical modeling in the framework of the problems of non-destructive testing of structural materials. A mathematical formulation of a three-dimensional problem of diagnostics for elastic layered medium is constructed, which makes it possible to determine the spatial distribution of residual stresses from the values of displacements measured on the surface of a layered half-space, which arose as a result of a specially initiated wave process. Under the assumption of weak inhomogeneity and anisotropy of the layers, a transition is made to a linearized (which is ill-posed) problem, the procedure for solving which is constructed using the method of stationary basic processes. As an example, the case of diagnosing a one-dimensional (depending only on the distance to the surface) distribution of residual stresses is considered.
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