 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 13088 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8125
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| In English (Mech. Solids): | | 4963 |
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| I.V. Kirillova, "Asymptotic Method in Problems of Elliptic Boundary Layer in Shells of Revolution under Impacts of Normal Type," Mech. Solids. 60 (1), 103-111 (2025) |
| Year |
2025 |
Volume |
60 |
Number |
1 |
Pages |
103-111 |
| DOI |
10.1134/S0025654424605524 |
| Title |
Asymptotic Method in Problems of Elliptic Boundary Layer in Shells of Revolution under Impacts of Normal Type |
| Author(s) |
I.V. Kirillova (Saratov State University, Saratov, 410012 Russia, iv@sgu.ru) |
| Abstract |
The asymptotic method for studying the behavior of non-stationary waves in thin shells generally involves using the separation method of solutions in the phase plane into components with different indices of variability in coordinates and time. In the case of normal type of impact, one of these
components is an elliptical boundary layer occurring in a small neighborhood of the surface Rayleigh
wave front. Its equations are derived by the method of asymptotic integration from the three-dimensional equations of elasticity theory. And they are partial differential equations of elliptic type with
boundary conditions specified by hyperbolic equations. The article presents a general asymptotic
method for solving the equations of the boundary layer under consideration in the case of the arbitrary
form shell of revolution as an example. It is based on a preliminary study of basic problems for shells
of revolution of zero Gaussian curvature using integral Laplace and Fourier transforms. The equations
of this boundary layer for different types of normal loading have a common characteristic property: the
asymptotically principal components coincide with the corresponding equations for shells of revolution of zero Gaussian curvature. This property, together with the property of different variability of the
components of the SSS and geometric parameters, allows, when using the method of exponential representations in the Laplace transform space, to functionally relate the solutions in the case of the arbitrary form shell of revolution with the solutions for shells of revolution of zero Gaussian curvature. The
developed general approach is applied in this article to solving the problem of an elliptical boundary
layer in shells of revolution under normal type loading. A numerical calculation of the shear stress for
the obtained asymptotic solution in the case of a spherical shell is given. |
| Keywords |
asymptotic method, elliptical boundary layer, shell of revolution, shear stress, Rayleigh surface waves front, method of exponential representations, Laplace transform, Fourier transform |
| Received |
24 September 2024 | Revised |
30 September 2024 | Accepted |
30 September 2024 |
| Link to Fulltext |
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