Elliptic boundary layer in shells of revolution under surface shock loading of normal type
- 作者: Kirillova I.V.1
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隶属关系:
- Saratov State University
- 期: 编号 5 (2024)
- 页面: 48–59
- 栏目: Articles
- URL: https://journals.rcsi.science/1026-3519/article/view/277074
- DOI: https://doi.org/10.31857/S1026351924050045
- EDN: https://elibrary.ru/UBBQQG
- ID: 277074
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详细
This article presents a method for solving the boundary-value problem for an elliptic boundary layer occurring in thin-walled shells of revolution under impact loads of normal type applied to the face surfaces. The elliptic boundary layer is formed in the vicinity of the conditional front of Rayleigh surface waves and is described by elliptic equations with boundary conditions determined by hyperbolic equations. In the general case of shells of revolution, methods for solving elliptic boundary layer equations developed for shells of revolution with zero Gaussian curvature cannot be applied. The previously considered approach using Laplace and Fourier integral transforms fails because the governing equations become equations with variable coefficients. The method proposed in this article for solving the equations of the elliptic boundary layer is based on the use of asymptotic representations of the Laplace-transformed solutions (in time) in exponential form. Numerical calculations of normal stresses based on the obtained analytical solutions are provided for the case of a spherical shell.
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参考
- Nigul U. Regions of effective application of the methods of three-dimensional and two-dimensional analysis of transient stress waves in shells and plates // Int. J. Solid and Structures. Vol. 5. № 6. 1969. P. 607–627.
- Nigul U. Comparison of the results of the analysis of transient wave processes in shells and plates according to the theory of elasticity and approximate theories // Applied Mathematics and Mechanics. 1969. Vol. 33. Issue 2. Pp. 308–332.
- Gol’Denveizer A.L. Theory of Elastic Thin Shells // Pergamon. 1961, p. 680.
- Gol’Denveizer A.L., Lidskiy V.B., Tovstik P.E. Free vibrations of thin elastic shells. 1979. 384 p.
- Kaplunov Yu.D., Kirillova I.V., Kossovich L.Yu. Asymptotic integration of the dynamic equations of the theory of elasticity for the case of thin shells. J. Appl. Math. Mech. Volume 57, Issue 1, pp. 95–103.
- Kossovich L.Yu. Non-stationary problems of the theory of elastic thin shells. Saratov, 1986, 176 p.
- Kaplunov J.D., Nolde E. V., Kossovich L.Y. Dynamics of thin walled elastic bodies // Academic Press. 1998. P. 226.
- Kirillova I.V., Kossovich L.Y. Asymptotic theory of wave processes in shells of revolution under surface impact and normal end actions Mechanics of Solids. 2022. Т. 57. № 2. P. 232–243.
- Kirillova I.V., Kossovich L.Y. refined equations of elliptic boundary layer in shells of revolution under normal shock surface loading. Vestnik of the St. Petersburg University: Mathematics. 2017. Т. 50. № 1. С. 68–73.
- Kaplunov Yu.D., Kossovich L.Yu. Asymptotic model for calculating the far field of a Rayleigh wave in the case of an elastic half-plane. Reports of the Academy of Sciences. 2004. Vol. 395. No. 4. Pp. 482–484.
- Polyanin A.D., Manzhirov A.V. Handbook of integral equations. 2nd ed. Chapman & Hall/CRC Press. 2008. P. 1108.
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