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The finite difference technique of calculation of axisymmetrical dynamic deformation of shells - empty and interacting with elastic (viscous-elastic) core is developed. The conditions of anchorage, filamentary - stratified structure of shell, viscous-elastic property of core material, real geometry of construction are taken into account. These properties are characteristic of the defined class of rigid fuel motors. The series of the new tasks of dynamics of isotropic and composite shells of revolution with elastic and viscous-elastic core is decided. The response of isotropic cylindrical shell on instantly affixed strength on the end face for long slice of times with using of characteristic difference scheme is investigated. The area of applicability of the difference scheme "cross" in the problem of impulse loading of the end face is appreciated. Together with Ganeeva M.S., Moiseeva V.E. the stress-strain state of spherical, ellipsoidal, cylindrical shells under the action of power loads, temperature, and fluid pressure is investigated.
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