Geodesic
Asymptotic methods in dynamics of shells under shock loading
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 8 (2008) no. 2, pp. 12-33

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The paper deals with the asymptotic methods, developed for creating a mathematic model of non-stationary wave propagation in shells of revolution under shock impacts of tangential, bending types and shock impacts of normal type; the methods are also aimed at solving the boundary value problems for the strain-stress state (SSS) components with different values of variability and dynamicity indices. Classification of asymptotic approximations is also presented. This classification defines three different types of separation scheme of non-stationary SSS. This scheme uses the following asymptotic approximations: short-wave and low-frequency ones, boundary layers in the vicinities of the quasi-front, the dilatation and shear wave fronts, and the front of Rayleigh surface waves. The schemes of ranges of applicability of approximate theories and schemes for the longitudinal stress resultant, bending moment and transverse shear force are represented. 
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     author = {L. Yu. Kossovich},
     title = {Asymptotic methods in dynamics of shells under shock loading},
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L. Yu. Kossovich. Asymptotic methods in dynamics of shells under shock loading. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 8 (2008) no. 2, pp. 12-33. http://geodesic.mathdoc.fr/item/ISU_2008_8_2_a1/