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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 86
Edited by: B.H.V. Topping
Paper 109

Non-Stationary Asymptotic Analysis of Combined and Stiffened Shells

L.Yu. Kossovich and I.V. Kirillova

Department of Mechanics and Mathematics, Saratov State University, Russia

Full Bibliographic Reference for this paper
L.Yu. Kossovich, I.V. Kirillova, "Non-Stationary Asymptotic Analysis of Combined and Stiffened Shells", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 109, 2007. doi:10.4203/ccp.86.109
Keywords: asymptotic, approximations, propagation of waves, combined and stiffened shells, stress strain state, overlap regions.

A review of papers devoted mathematical modeling of non-stationary wave propagation in combined and stiffened shell structures (on the base of shells of revolution) using asymptotic methods applying to exact three-dimensional equations of elasticity theory is presented.

Transient waves in shells of revolution initiated by tangential and bending longitudinal shock loading are considered. An asymptotic model of wave propagation in a semi-infinite shell of revolution (a version of method of matched asymptotic expansions) is used. The choice of approximations is connected with different values of variability and dynamicity indices [1,2]. We used following approximations: long-wave low-frequency approximations (tangential and transverse), the Saint-Venant quasi-static boundary layer, the quasi-plane problem of elasticity (quasi-symmetric and quasi-antisymmetric), as well as boundary layers within vicinities of the wave fronts and quasi-front. The accuracy of this separation of non-stationary stress strain state (SSS) has previously been established by demonstrating the existence of the overlap regions between the various approximations. In particular, it has been shown that overlap regions exist between the long-wave tangential approximation and the boundary layer in the vicinity of the quasi-front; the long-wave transverse approximation and the solution of the quasi-plane quasi-anti-symmetric problem; and solution of the quasi-plane problems and the boundary layers in the vicinities of the dilatation wave front [1,2,3].

L.Yu. Kossovich, "Non-stationary Problem in Theory of Elastic Thin Shells" (in Russian), Saratov University Press, Saratov, Russia, 1986.
J.D. Kaplunov, L.Yu. Kossovich and E.V. Nolde, "Dynamics of Thin Walled Elastic Bodies", Academic Press, San Diego, 1998.
I.V. Kirillova, "Ranges of applicability of boundary layers in vicinities of wave fronts in shells of revolution of zero Gaussian curvature" (in Russian), Journal of Izv. RAN Ser. Mekhanika Tverdogo Tela, 38, N6, 117-125, (English Transl. Mechanics of Solids, 38), 2003.

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