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On the deformation of coated functionally graded structures with delamination

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Abstract

The paper considers problems for extensional inhomogeneous layered structures with functionally graded coatings in the presence of delamination. An approach that allows, from a single point of view, to study the problem of equilibrium of a strip non-uniform along the vertical coordinate with a delaminated coating and the problem of steady-state oscillations of a cylindrical waveguide with a ring crack is developed. Using the Fourier transform, the problems for the strip and waveguide are reduced to canonical systems of differential equations with variable coefficients with respect to transformants of the stress tensor components and displacement vector. Based on the formulation of several auxiliary Cauchy problems, a scheme for constructing a system of integral equations with hypersingular kernels with respect to jumps of displacements on the banks of delamination is presented. The asymptotic behavior of the Fourier symbols of kernels of integral operators for large values of the transformation parameter is investigated. A computational scheme for solving the system of integral equations based on the boundary element method is developed. The results of computational experiments on the determination of the disclosure functions of the delamination banks for a strip and a waveguide in the presence of a discontinuity in the elastic moduli at the boundary of the main body and the coating are presented.

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Acknowledgements

The work was supported by a Grant from the Government of the Russian Federation No. 075-15-2019-1928.

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Authors and Affiliations

  1. Institute of Mathematics, Mechanics and Computer Science named after I. I.Vorovich, Southern Federal University, Rostov-on-Don, Russian Federation

    A. O. Vatulyan, D. K. Plotnikov & V. O. Yurov

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  1. A. O. Vatulyan
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  2. D. K. Plotnikov
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  3. V. O. Yurov
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Correspondence to D. K. Plotnikov.

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Vatulyan, A.O., Plotnikov, D.K. & Yurov, V.O. On the deformation of coated functionally graded structures with delamination. Acta Mech 232, 1863–1873 (2021). https://doi.org/10.1007/s00707-020-02846-w

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  • DOI: https://doi.org/10.1007/s00707-020-02846-w

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