For citation:
Kirillova I. V. Asymptotic theory of the hyperbolic boundary layer in shells of revolution at shock edge loading of the tangential type. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2024, vol. 24, iss. 2, pp. 222-230. DOI: 10.18500/1816-9791-2024-24-2-222-230, EDN: SFYWBV
Asymptotic theory of the hyperbolic boundary layer in shells of revolution at shock edge loading of the tangential type
The present work is devoted to the construction of asymptotically optimized equations of the hyperbolic boundary layer in thin shells of revolution in the vicinity of the dilation wave front at shock edge loading of the tangential type. These equations are derived by asymptotically integrating of the exact three-dimensional theory elasticity equations in the special coordinate system. This system defines the boundary layer region. The wave front has a complicated form, dependent on the shell curvature and therefore its asymptotical model is constructed. This geometrical model of the front defines it via the turned normals to the middle surface. Also, these turned normals define the geometry of the hyperbolic boundary layer applicability region. Constructed asymptotically optimised equations are formulated for the asymptotically main components of the stress-strain state: the longitudinal displacement and the normal stresses. The governing equation for the longitudinal displacement is the hyperbolic equation of the second order with the variable coefficients. The asymptotically main part of this equation is defined as the hyperbolic boundary layer in plates.
- Nigul U. K. Regions of effective application of the methods of three-dimensional and two-dimensional analysis of transient stress waves in shells and plates. International Journal of Solids and Structures, 1969, vol. 5, iss. 6, pp. 607–627. https://doi.org/10.1016/0020-7683(69)90031-6
- Kossovich L. Yu. Nestatsionarnye zadachi teorii uprugikh tonkikh obolochek [Unsteady Problems in the Theory of Elastic Thin Shells]. Saratov, Saratov State University Publ., 1986. 176 p. (in Russian). EDN: VIOSWL
- Kaplunov Y. D., Kossovich L. Yu., Nolde E. V. Dynamics of Thin Walled Elastic Bodies. San Diego, Academic Press, 1998. 226 p. https://doi.org/10.1016/C2009-0-20923-8, EDN: WNSAFB
- Kossovich L. Yu, Kirillova I. V. Dynamics of shells under shock loading: An asymptotic approach. Civil-Comp Proceedings, 2008, vol. 88, pp. 1–20. EDN: QPMORG
- Kossovich L. Yu., Kirillova I. V. Asymptotic theory of nonstationary processes in thin shells. Proceedings of the Second International Conference Topical Problems of Continuum Mechanics. Dilijan, Armenia, 2010, vol. 1, pp. 321–325 (in Russian).
- Kirillova I. V., Kossovich L. Yu. Dynamic boundary layer at nonstationary elastic wave propagation in thin shells of revolution. AiM’96: Proceedings of the Second International Conference “Asymptotics in mechanics”. Saint Petersburg State Marine Technical University, Saint Petersburg, Russia, October 13–16, 1996. Saint Petersburg, 1997, pp. 121–128.
- Kirillova I. V. Asymptotic derivation of two types of approximation of dynamic equations of the theory of elasticity for thin shells. Diss. Cand. Sci. (Phys.-Math.). Saratov, 1998. 122 p. (in Russian).
- Goldenweiser A. L. Teoriya uprugikh tonkikh obolochek [Theory of Elastic Thin Shells]. Moscow, Nauka, 1976. 512 p. (in Russian).
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