Numerical Investigation of the Dynamics of Thick-Walled Cylindrical Shells with a Helical Reinforcement

The Wilkins method is modified for numerically investigating the dynamics of thick-walled cylindrical shells with a helical orthotropy. The results of calculations by this algorithm agree well with known analytical solutions. Some new physical effects, which are absent in isotropic and cylindrically orthotropic shells, are investigated.__________Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 2, pp. 225–236, March–April, 2005.     

Stress state of orthotropic shells with a straight slit

A shallow orthotropic shell of arbitrary curvature with a straight slit is examined. Results are presented to describe the numerical effect of the curvature of the shell and the length and orientation of the slit on the stress and moment intensity factors in orthotropic shells made of various orthotropic materials.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 18, pp. 63–65, 1987.     

Behavior of composite cylindrical shells subjected to nonuniform heating

Nonlinear differential equations describing the thermoelastic behavior of closed orthotropic circular shells under nonuniform heating conditions are obtained; the temperature dependence of the elastic parameters of the material is taken into account. The problem of the stability of a glass-reinforced plastic shell hinged to fixed supports and heated nonuniformly over the thickness is solved. The results of tests on 27–63SV glass-reinforced plastic shells heated and subjected to additional compressive loads at various levels are presented. The theoretical and experimental data are compared.Zukovskii Air Force Engineering Academy. Translated from Mekhanika Polimerov, No. 2, pp. 284–292, March–April, 1971.     

Dynamic stability of axisymmetrically heated glass-reinforced plastic cylindrical shells bonded to elastic cylinders

The dynamic stability of glass-reinforced plastic shells subjected to the action of a longitudinal pulsating force and an external, uniformly distributed load is examined. The shells are orthotropic, and their elastic properties are temperature-dependent and vary over the thickness of the wall. It is assumed that the elastic cylinder forms a Winkler foundation. Three boundary conditions are investigated.Moscow Institute of Chemical-Machine Building. Translated from Mekhanika Polimerov, No. 2, pp. 331–337, March–April, 1972.     

Stability of cylindrical glass-reinforced plastic shells under external pressure

The stability of cylindrical glass-reinforced-plastic shells under external omnidirectional hydrostatic pressure has been the subject of an experimental investigation. The experimental data obtained are compared with calculations based on the theory of orthotropic shells.Mekhanika Polimerov, Vol. 3, No. 6, pp. 1089–1095, 1967     

Resolvents of the theory of orthotropic shells with low shear stiffness in force-moments and stress functions

The problem of the theory of orthotropic layered shells with low shear stiffness is reformulated in force-moments and stress functions on the basis of new strain continuity relations constructed with allowance for transverse shears.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 950–952, September–October, 1970.     

Investigation of the anisotropy of the properties of glass-reinforced plastic shells

The load-carrying capacity and deformation of cylindrical and conical glass-reinforced plastic (ÉDT-10 resin) shells loaded in axial compression have been investigated experimentally in relation to the orientation of the fabric reinforcement. The results of the tests are compared with the relations of the theory of elasticity of an orthotropic body.Zhukovskii Central Aerohydrodynamics Institute, Moscow Region; Scientific Research Institute of Production Technology and Organization, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 814–818, September–October, 1969.     

Influence of heating on the stability of fiberglass reinforced plastic shells during axial compression

Results are described of the experimental investigation of the patterns of change of carrying capacity and deformation of smooth thin-walled round cylindrical shells made from fiberglass reinforced plastic based on phenol-formaldehyde binder, loaded by an axial compressing force in a temperature field uniform with respect to the thickness of the wall and the surface. The experimental data are compared with calculated ones obtained according to the formulae of the theory of orthotropic shells. The influence of circumferential compressing stresses arising in the junction zone of the heated wall with less heated thicker parts at the edges (ribs) on the carrying capacity of the shells is evaluated.Professor N. E. Zhukovskii Central Aerodynamics Institute, Moscow Oblast. Translated from Mekhanika Polimerov, No. 5, pp. 838–845, September–October, 1972.     

Variant of the geometrically nonlinear theory of anisotropic shells with allowance for transverse shear

A very simple variant of the geometrically nonlinear theory of anisotropic shells with allowance for the high compliance of the material in transverse shear is proposed. From this theory there follow, as a special case, the equations for an isotropic shell; these differ from the relations of [2] with respect to terms of the order of the ratio of the thickness of the shell to the radii of curvature small as compared with unity. The equations obtained are used to solve the problem of the stability of orthotropic shells of revolution relative to the starting axisymmetric state of stress.Translated from Mekhanika Polimerov, No. 5, pp. 863–871, September–October, 1969.     

State of stress deformation of an orthotropic fiberglass shell in consideration of the creep of the material

Based on Volterra's principle we analyzed the axisymmetrical curvature of cylindrical orthotropic shells under the effect of sustained external pressure in consideration of the creep due to interlaminar shift. To solve the viscosity-elasticity problem, the known elastic solution is approximated by means of simple analytical dependences, taking the lateral shifts into account. Numerical examples are presented.Translated from Mekhanika Polimerov, No. 3, pp. 552–555, May–June, 1970.     

Stability of orthotropic cylindrical shells under variable pressure

A method of determining the critical stresses is developed for elastic orthotropic cylindrical shells subjected to nonuniform pressure. It is assumed that the external pressure varies over the cross section and is constant along the length of the cylinder. A shell stability analysis is given for the case of a weakly varying load.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 5, pp. 897–902, September–October, 1970.     

Numerical analysis of axisymmetric oscillations of an orthotropic cylindrical shell

The frequency spectrum of shells is analyzed by numerical methods using three-dimensional and applied theories. The axisymmetric oscillations of an orthotropic cylindrical shell with Navier conditions on the edges are investigated. The effect of boundary conditions on the frequency spectrum is also studied numerically.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 55, pp. 106–109, 1985.     

Effect of the stiffness of the elastic core on the buckling mode and the critical load for glass-reinforced plastic cylindrical shells in axial compression

The effect of the stiffness of the core, treated as a three-dimensional elastic body, on the buckling mode and the critical load is investigated for orthotropic cylindrical shells in axial compression. Parametric equations that permit the easy determination of the critical loads are obtained together with an expression for the stiffness parameter at which the buckling mode changes. The effect on the critical load of a central opening in the core is considered.Translated from Mekhanika Polimerov, No. 5, pp. 931–939, September–October, 1971.     

Stability of composite shells with an elastic core

The stability in axial compression of orthotropic cylindrical shells with an elastic core is investigated with allowance for the following factors: transverse shear strains in the shell material, precritical state of stress of the core, and the moments due to the surface forces exerted on the shell by the core. The numerical results obtained are compared with the results of approximate methods in which the above-mentioned factors are disregarded.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 3, pp. 544–547, May–June, 1976.     

The shell theory including transverse shear deformations and thickness change

A variational method for refining the theory of shells based on power series expansion of displacements has been described. The particular case of a cubic approximation for the tangential displacements and a quadratic approximation for the deflections is considered in detail. A constitutive system of differential equations in the canonical form for the axisymmetrical deformation of cyclindrical shells is derived. As an example, axisymmetrical deformations of a cylindrical shell made of an orthotropic composite material are discussed.Martin Luther Universität Halle-Wittenberg, Fachbereich Werkstoffwissenschaften. Germany. Kharkov State Polytechnical University, Department of Dynamics and Strength of Machines. Ukraine. Published in Mekhanika Kompozimykh Materialov, No. 6, pp. 768–780. November–December, 1997.     

Optimization of a cylindrical shell of reinforced plastic with a filler under dynamic loading

Conclusions 1. The numerical investigation of profiles of functions of the physical constraints carried out in this work allows us to assume that problems of optimal design of shells of reinforced plastics, strengthened by an elastic filler, for purposes of stability (static and dynamic) under axial compression, in the given formulation, are problems of convex programming. This guarantees uniqueness of their solution and allows us to use gradient methods for a numerical realization.2. Optimal shells of a composite material have a smaller mass than equivalent shells of high-strength metal alloys. The gain in the expenditure of the material is ensured not only as a result of higher specific characteristics of the composite, but basically as a result of optimizing the reinforcement structure of the pack of orthotropic layers of the shell.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 879–885, September–October, 1977.     

Numerical solution of problems of statics of variable-rigidity flexible spherical shells

A method is developed for numerical solution of nonlinear two-dimensional boundary-value problems of statics describing unsymmetric strain of flexible orthotropic layered spherical shells of variable rigidity in classical and enhanced-accuracy formulations. Dimension reduction is achieved by enhanced-accuracy finite-difference approximation combined with the quasilinearization method and a stable numerical method of solution of one-dimensional linear boundary-value problems.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 73, pp. 61–66, 1992.     

Strain of a flexible orthotropic cylindrical shell as a function of orthotropy parameters

A procedure is proposed for calculating the stress-strain state of flexible orthotropic cylindrical shells of constant thickness with unsymtnetric load and nonhomogeneous boundary conditions. The system of nonlinear partial differential equations is solved by the method of lines. The system of nonlinear ordinary differential equations is reduced by linearization to a sequence of linear systems. The sequence of linear boundary-value problems is solved by the discrete orthogonalization method.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 59, pp. 57–61, 1986.     

The theory of orthotropic layered cylindrical shells

The author examines orthotropic layered cylindrical shells for which the moduli of elasticity of the load-carrying layers substantially exceed the shear modulus between layers. This class of structure includes, in particular, shells made of orthotropic glass-reinforced plastic. In this case the classical theory based on the Kirchhoff-Love hypotheses requires refinement; the corresponding equations obtained as a result of approximating the distribution of shear stresses or displacements over the thickness of the shell by a certain known function are presented in [4, 7, 8]. In this paper equations that make it possible to construct the stress distribution over the shell thickness are obtained within the framework of the engineering theory on the basis of the hypothesis of the incompressibility of a normal element.Mekhanika Polimerov, Vol. 4, No. 1, pp. 136–144, 1968     

Stress distribution in orthotropic shells of revolution with allowance for nonlinear factors

Basic relations and resolvent equations of a theory of orthotropic shells of revolution are presented with allowance for both geometric and physical nonlinearity. The approach to solve nonlinear problems is based on the methods of successive approximation and finite differences. A numerical study is made of the stress state of a spherical glass-plastic segment subjected to internal pressure. Solutions of problems are presented for linear and nonlinear (with allowance for one or two nonlinearities) formulations. The results obtained are analyzed.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 18, pp. 76–78, 1987.