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DOI: 10.46698/k5003-0293-2639-b
Inverse Problem of Delamination Reconstruction in a Functionally-Graded Strip
Yavruyan, O. V.
Vladikavkaz Mathematical Journal 2026. Vol. 28. Issue 3.
Abstract: The steady-state oscillations of a functionally graded strip weakened by tunnel delaminations at its lower boundary are studied. The direct problem of constructing the wave field throughout the strip is solved. Its solution is obtained by reduction to a boundary integral equation (BIE) with respect to the unknown components of the delamination opening displacement function. This function is nonzero only within the zone of defects. The boundary value problem with variable coefficients for the transformed displacement and stress fields is solved using the shooting method. An analysis of the BIE kernel is performed. The asymptotic behavior of the symbol of the kernel at infinity is investigated, yielding an analytical estimate that allows separation of the BIE kernel into regular and irregular (singular) parts. Discretization of the BIE is implemented using the boundary element method (BEM), collocation methods, and numerical quadrature schemes for singular integrals. The inverse problem of delamination identification is reduced to determining the invariant parameters of the defect through minimization of a residual functional, using zero-order optimization algorithms (genetic algorithm, Nelder-Mead method). An asymptotic analysis is performed for defects of small relative sizes. The inverse problem of crack parameter identification is solved using displacement field data measured on a portion of the upper boundary of the strip. A comparative analysis is conducted of the results obtained via BEM and the asymptotic approach. The applicability limits of asymptotic formulas are established.
For citation: Yavruyan, O. V. Inverse Problem of Delamination Reconstruction in a Functionally-Graded Strip, Vladikavkaz Math. J., 2026, vol. 28, no. 3, pp.134-149 (in Russian). DOI 10.46698/k5003-0293-2639-b
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