On the deformation of coated functionally graded structures with delamination
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O R I G I NA L PA P E R
A. O. Vatulyan
· D. K. Plotnikov
· V. O. Yurov
On the deformation of coated functionally graded structures with delamination
Received: 13 June 2020 / Revised: 15 September 2020 / Accepted: 23 September 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
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. 1 Introduction Currently, materials which are characterized by a change in the mechanical properties with the coordinate are widely used in engineering practice. Multilayer constructions are used; technologies for the creation of functionally graded materials (FGM) with continuous change in properties are being actively developed [1]. The absence of discontinuities in the properties of the material allows to avoid the formation of stress concentration regions and improves the strength characteristics of fabricated structural elements, which reduces the chance of cracking and delamination. Modeling of objects with substantially inhomogeneous properties requires studying the deformation of inhomogeneous layered structures under static and dynamic influences. When modeling objects such as pipelines, blood vessels, etc., cylindrical structures inhomogeneous in the radial direction are increasingly used. When describing the propagation of waves in inhomogeneous structures at high frequencies, models A. O. Vatulyan · D. K. Plotnikov (B) · V. O. Yurov Institute of Mathematics, Mechanics and Computer Science named after I. I.Vorovich, Southern Federal University, Rostov-onDon, Russian Federation E-mail: [email protected] A. O. Vatulyan E-mail: [email protected] V. O. Yurov E-mail: [email protected]
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