Solution of two-dimensional boundary-value problems of the theory of thin composite shells

Discrete analogues of the boundary-value problems of a two-dimensional refined theory of anisotropic shells taking into account the transverse shear deformation are presented. The systems of resolving equations in the general form are obtained for arbitrary nonshallow shells of variable curvature whose coordinate lines of the reduction surface may not coincide with the lines of principal curvatures. The algebraic problems of determining the stress-strain state in shells made of composite materials with stress concentrators under various kinds of loads are obtained as particular cases of the schemes presented. The results of calculating the stress concentration near a nonsmall circular hole in a transversely isotropic nonshallow spherical shell under internal pressure are presented. The dependences of stress concentration factors on the hole dimension and on a change in the shear stiffness of the shells are studied. A comparison between the calculation results obtained within the framework of the theories of shallow and nonshallow shells is given.Presented at the 11th International Conference on the Mechanics of Composite Materials (Riga, June 11–15, 2000).Timoshenko Institute of Mechanics, Ukranian National Academy of Sciences, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 4, pp. 465–472, July–August, 2000.     

Vibrations of isotropic viscoelastic shells

It is shown that the boundary value problems for viscoelastic and elastic shells coincide. The natural and forced vibrations of shells are investigated by the averaging method.Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 1, pp. 157–163, January–February, 1971.     

Strain continuity equations in Timoshenko-type shell theory

The general linear continuity equations for shells for which the Timoshenko shear model is used as the kinematic relations are derived in tensor form. Particular cases of the continuity equations are considered for shells with the lines of principal curvature as coordinates and for cylindrical shells.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 105–109, January–February, 1973.     

Failure of water-filled cylindrical glass-reinforced epoxy shells under internal impulsive loading

Conclusions 1. The explosive failure of water-filled, geometrically similar glass-reinforced epoxy shells, whose dimensions increase by a factor of 1.5–4.4, is not associated with an energetic scale effect. This is attributable to the imperfect similarity of the shells, since although their dimensions changed, the diameter of the glass reinforcing fibers remained the same.2. The relative mass of explosive required to fracture the shells is approximately 0.4%. With respect to this index, glass-reinforced epoxy is comparable to structural steels 20 and 17Mn1Si at R₀160 mm.3. The circumferential deformation of the shells at failure is about 4% and does not depend on the thickness of the shell wall, the dimensions of geometrically similar shells, or the initial strain rate on the interval 0.21 · 10³–1.2 · 10³ sec^–1. Thin-walled shells begin to fail from the outside surface, thick-walled shells from the inside surface.4. The modulus of elasticity of the GRE is 2.4 · 10⁵ kgf/cm² and does not depend on the strain rate on the interval 10^–3–1.5 · 10³ sec^–1. The material deforms elastically up to failure.Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 283–289, March–April, 1978.     

Experimental methods of investigating the state of stress of glass-reinforced plastic shells

A method of testing glass-reinforced plastic shells under external hydrostatic pressure is described together with a procedure for determining the elastic properties of the material of which the shell is composed. Test data on the strength and stability of shells subjected to external hydrostatic pressure are presented.Leningrad. Translated from Mekhanika Polimerov, Vol. 5, No. 1, pp. 157–163, January–February, 1969.     

Optimization of the axial stability of equal-strength reinforced cylindrical pressure vessels

The class of reinforced cylindrical shells obtained by spiral winding with reinforcing ring or longitudinal layers is considered. The structure of the shells is optimal with respect to internal pressure. The reinforcement angle is selected so as to maximize the critical axial load.Translated from Mekhanika Polimerov, No. 6, pp. 1123–1126, November–December, 1973.     

Stability of axially compressed cylindrical composite shells in the presence of nonstationary heating

The problem of smooth cylindrical composite shells uniformly compressed in the axial direction and subjected to nonstationary heating is solved in the linear quasi-static formulation. Expressions are obtained for the critical loads and their regions of application are determined. The calculations are compared with experimental data obtained by linearly heating the outer surface of axially compressed smooth cylindrical shells of glass-reinforced plastic based on phenol-formaldehyde resin.Zhukovskii Central Aerohydrodynamic Institute, Moscow Region. Translated from Mekhanika Polimerov, No. 2, pp. 289–297, March–April, 1973.     

Analysis of free damped vibrations of laminated composite cylindrical shells

Damped free vibrations of multilayered composite cylindrical shells are investigated. Vibration and damping analysis of cylindrical shells is performed by using the first-order shear deformation theory (FOSDT). Based on other researchers' works, two damping models are developed, i.e., the energy method (EM), and the method of complex eigenvalues (MCE). Several numerical examples of the damped free vibration problem of laminated composite cylindrical shells have been solved and comparison has been made with the results of other authors.Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 5, pp. 646–659, September–October, 1995.     

Effect of the two-way reinforcing system on the load-carrying capacity of glass-reinforced plastic shells

The load-carrying capacity of thin cylindrical glass-reinforced plastic shells loaded by axial compression and external pressure has been investigated in relation to the characteristics of the two-way reinforcing system. The critical loads are expressed in terms of the characteristics of a parallel-reinforced layer with a coefficient that takes into account the reinforcing system and the shape of the cross section. The relations among the reinforcing layers optimal for the load-carrying capacity are determined and it is shown that independent two-way reinforcing substantially improves the load-carrying capacity of solid shells and shells with a nonload-bearing core.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 6, pp. 1052–1058, November–December, 1969.     

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.     

Stresses in adhesive joints in cylindrical shells and panels

The stresses in adhesive joints in cylindrical shells and panels are determined for the general case of loading. The effects of joint length and the parameters of the adhesive, the shells, and the panels on the magnitude of these stresses are investigated.Aviation Technology Institute, Moscow. Translated from Mekhanika Polimerov, No. 6, No. 1093–1103, November–December, 1972.     

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.     

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.     

Modeling process operations in the forming of parts made of flat metal-polymer composites

The forming of complex three-dimensional parts (tubular structures, sections, shells) from flat sheets of metal-polymer composites is examined. Results are reported from a series of experimental studies of the strain and strength characteristics of these composites, and features of the fabrication of shells of single and double curvature are analyzed. One method of solving the problem of bending shells of complex shape with large displacements (deflections) beyond the elastic limit of the material is proposed and substantiated empirically.Paper to be presented at the IX International Conference on the Mechanics of Composite Materials (Riga, October, 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 3, pp. 417–427, May–June, 1995.     

Some mechanical properties of film-reinforced plastics

Model cylindrical shells have been wound from glass and Dacron (Mylar) film strip in accordance with a technique developed by the authors. A layer of glass-reinforced plastic, oriented in the direction of the circumferential tensile stresses, was applied to the outer cylindrical surface of the shells. Certain mechanical properties of the film plastics and their ability to cooperate with the glass-reinforced plastic outer layer were investigated by subjecting the shells to internal liquid pressure. The possibility of obtaining impermeable shells, equally strong in the axial and circumferential directions, was confirmed.Bauman Moscow Higher Technical College. Translated from Mekhanika Polimerov, No. 1, pp. 135–139, January–February, 1971.     

Critical compressive stresses in cylindrical shells composed of orthotropic layers with different orientations

The laws of variation of the strains and critical stresses for smooth thin circular cylindrical glass-reinforced plastic shells based on ÉDT-10P resin have been experimentally investigated at different orientations of the fabric reinforcement. The results of the tests are compared with the theoretical data obtained from the relations of the theory of elasticity of an orthotropic body and orthotropic shells.N. E. Zhukovskii Central Aerohydrodynamic Institute of Production Technology and Organization, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 684–690, July–August, 1973.     

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     

Rationalization of the shape of wound membrane shells of revolution composed of high-modulus material

A method of designing composite membrane shells of revolution under axisymmetric loading is described. The properties of the shell material are analyzed. It is shown that for shells of high-modulus material in the presence of tensile membrane stresses the fibers fail in the matrix. A fiber arrangement and shell geometry ensuring isotensoid properties are proposed for this case. A technological and weight analysis is presented.S. Ordzhonikidze Moscow Aviation Institute. Translated from Mekhanika Polimerov, No. 5, pp. 822–828, September–October, 1975.     

Analysis of glass-reinforced plastic bottoms of cylindrical pressure vessels

Solutions are proposed for boundary value problems associated with spherical, ellipsoidal and optimal-design glass-reinforced plastic bottoms filament-wound as an integral part of cylindrical shells.Moscow Region. Translated from Mekhanika Polimerov, Vol. 4, No. 5, pp. 918–926, September–October, 1968.     

Some problems of the theory and analysis of anisotropic plates and shells with low shear stiffness

Certain problems associated with the theory and analysis of plates and shells made of materials with low shear stiffness are discussed.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov. Translated from Mekhanika Polimerov, No. 4, pp. 693–714, July–August, 1970.