Numerical studies on the dynamic behavior of multilayer thick-walled cylinders with helical orthotropy

Abstract

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...

A numerical study of the nonlinear dynamics of multilayer spirally orthotropic cylinders

“…In [5], the method for the numerical study of the dynamics of multilayer thick-walled elastic cylindrical shells with different spiral reinforcement structures was developed on the basis of the Wilkins two-dimensional algorithm and the specific features in the dynamic behavior of a two-layer cylinder were studied for different spiral reinforcement configurations.…”

“…The aim of the present paper is to generalize the methods [5,6] to the case of the axisymmetrical dynamic loading of thick-walled multilayer spirally orthotropic elastoplastic cylinders taking into account the geometrical and physical nonlinearities, as well as to study the effect of various reinforcement configurations and nonlinearity types on the SSS of thick-walled single-and two-layer cylindrical shells subjected to the action of the axisymmetric pulse loading.…”

“…The initial conditions were assumed to be zero, the boundary ones were regarded as force or kinematic, and the contact between the layers as ideal. Despite the presence of all the components of displacements, stresses and strains, the boundary problem of (1)-(8) will be axisymmetric in the sense that none of its variables is dependent on the angular coordinate ϕ [3,5].…”

“…The method is based on the Wilkins finite-difference scheme that is explicit in time and integral interpolating in space. Here, the procedure [5] debugged for finite strains (including plastic ones) in accordance with the approach given in [6] was used as the basis.…”

Stress field of orthotropic cylinder subjected to axial compression

“…Jeffery et al [6] simulated biological soft tissue by the orthotropic hyper-elastic constitutive law. Romashchenko and Tarasovskaya [7] carried out numerical studies on the dynamic behavior of multilayer thick-walled cylindrical shells with different spiral reinforcement structures. Redekop [8] made use of differential quadrature methods to predict the buckling characteristics of an orthotropic shell of revolution of arbitrary meridian subjected to a normal pressure.…”