The Wilkins two-dimensional algorithm-based method of numerical studies on the dynamic behavior of multilayer thick-walled cylindrical shells with different spiral reinforcement structures is developed. Test calculations are in good agreement with known solutions. The dynamic behavior of a two-layer cylinder with different spiral reinforcement structures is investigated.The potentials and advantages of composite uses in the structures subjected to nonstationary effects (vessels, housings or protective constructions experiencing high internal hydro-or gas-dynamic loads, etc.) are presently well known [1-6]. One of the most important factors, determining their dynamic response and carrying capacity, is the reinforcement structure of the material. Multilayer structural components formed by local orthotropic layers and reinforced at certain angles to the cylindrical x, ϕ, r coordinates have received wide acceptance [7].The effect of different reinforcement structures of multilayer cylindrical glass fiber shells on their dynamic response and strength under internal explosive loading was experimentally studied elsewhere [8-10]. The reinforcement structure was established to exert a great influence on the response, carrying capacity, and fracture patterns of cylindrical shells. The combination of reinforcement structures with alternating annular and spiral layers of approximately equal thicknesses was noted to be preferential.Theoretical investigations of similar bodies under static loading are currently known, e.g., numerical analysis of the stress-strain state of a two-layer hollow cylinder subjected to external pressure [7]. The cylinder layers were reinforced with fibers oriented at equal but opposite angles about the longitudinal axis. It was established [7,11] that the studies on the stress-strain state should take account of the effects determined by the noncoincidence of principal elasticity directions and the direction of coordinate lines. The axisymmetric dynamics of a multilayer shell was numerically investigated in the shell approximation [12]. The results were presented for cylindrical shells formed by alternating spiral and annular layers of unidirectional glass fiber plastic and subjected to internal pulse pressure. Their analysis demonstrated that the stress state of the shell could be controlled by varying reinforcement angles and layer ratios.The literature review gives evidence that the major part of studies is devoted to investigating similar structures under static loading. The methods and results of numerical dynamic calculations for thick-walled bodies of rotation with cylindrical orthotropy are presented elsewhere [13][14][15][16]. The procedure is outlined to calculate natural frequencies of multilayer cylinders with helical orthotropy for the Navier boundary conditions at their ends [17]. The dynamic problems of the elasticity theory accounting for reinforcement structure effects on the stress-strain state of multilayer thick-walled hollow cylindrical bodies were not examined as far as the auth...

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Based on the Wilkins two-dimensional algorithm, a method is developed for the numerical study of the geometrically and physically nonlinear axially symmetrical dynamic stress-strain state of multilayer thick-walled cylindrical elastoplastic shells with different spiral reinforcement structures. A numerical study of the specific features in the nonlinear dynamic behavior of single-and two-layer cylinders is carried out for different reinforcement configurations and loading amplitudes.

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