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.     

State of stress of flexible plastic shells with an opening

The state of stress of flat flexible shells with an opening is investigated with allowance for the viscoelastic properties of the material. The equilibrium equations and boundary conditions are written in finite-difference form. A nonlinear system of algebraic equations is solved by successive approximations. A method of accelerating the convergence of slowly converging iteration processes is proposed. The effect of the viscoelastic properties of the shell material on its state of stress is investigated with reference to the example of a polymethyl methacrylate shell. The variations of the ring moment and ring forces at the free edge of the shell are plotted for various moments of time, load values, and flatness parameters. It is shown that as soon as the viscosity factor begins to take effect, the state of stress and strain of the shell changes sharply; the concentration of forces and moments increases in the flexible viscoelastic (as compared with the elastic) shell.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 6, pp. 1071–1075, November–December, 1973.     

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.     

Optimization of cyclindrical shells of fiber-reinforced composite materials

Problems of optimizing nonelastic circular shells are considered. The material of the shells is assumed to be a fiber-reinforced composite with fibers unidirectionally embedded in a relatively less stiff but ductile metallic matrix so that the material has the yield surface suggested by Lance and Robinson. The shell is subjected to an impulsive loading of short-time periods generating initial kinetic energy. During plastic deformation of the shell the initial kinetic energy is transformed into the plastic strain energy. The shell thickness is assumed to be piecewise constant. Various thicknesses and coordinates of the rings, where the thickness has jumps, are preliminarily unspecified. We look for a shell design for which the maximum residual deflection has a minimum value for the total weight given. The alternative problem of minimizing the shell weight for the maximum deflection given is also studied.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, Octobe, 1995.Tartu University, Estonia. Published in Mekhanika Kompozitnykh Materialov, No. 1, pp. 65–71, January–February, 1996.     

Propagation of Transient Hydroelastic Waves in a Semiinfinite, Piecewise-Constant Cylindrical Shell Containing a Fluid

A solution is formulated for a new problem of wave propagation in a semiinfinite cylindrical shell with a junction connecting two shells of different radii. The material of the shell is assumed to be viscoelastic, and the fluid is assumed to be viscous. The motion of the shell is described by Kirchhoff–Love theory, and the motions of the fluid are described by equations averaged over the cross section. The problem is solved by means of the time Laplace transform and subsequent numerical inversion. The numerical results for the pressure and radial displacement of the shell are analyzed for various values of the parameters.     

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.     

Strength and reliability of cylindrical shells prepared by the method of continuous filament winding

Conclusions 1. Strength calculation of shells whose material has a scatter in elastic and strength characteristics should be carried out using statistical methods. A deterministic calculation using values of elastic and strength characteristics leads to appreciable errors in the estimate of bearing ability.2. The problems of estimating the strength and the reliability of constructions from laminar composites are closely interconnected.3. Physicomechanical characteristics of a material which have been obtained in tests of unidirectional specimens make it possible to describe the behavior of a construction on the condition that the structure of the shell layer material is reduced to the structure of the specimen material.4. Allowing for the scale effect plays an important role in estimating the reliability and bearing ability of heavy-duty shells for large-size pressure vessels.Translated from Mekhanika Polimerov, No. 3, pp. 443–451, May–June, 1978.     

Theoretical and experimental study of the elastoplastic state of cylindrical shells with rigid inclusions

A study is made of the stress distribution around a rigid circular inclusion on the lateral surface of a cylindrical shell subjected to a uniformly distributed load. The stress distribution present during the elastoplastic stage of deformation of the shell material is studied. Calculated results are obtained on the basis of the numerical solution of inelastic problems in accordance with the theory of thin shells and the strain theory of plasticity for the case of active loading. Experimental data for shells loaded by internal pressure are obtained with the use of pneumatic gauges. The data are in the form of values of the strains and changes in curvature in characteristic sections of the shell. The theoretical and experimental results are compared and analyzed.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 18, pp. 72–76, 1987.     

Stress concentrations around openings in transversely isotropic shells

A method of investigating stress concentrations around openings in shells made of a transversely isotropic material (oriented glass-reinforced plastic [5]) is described. The use of a Timoshenko-type theory makes it possible to take into account the effect of tangential shearing stresses and the anisotropy of the elastic properties of the shell in a direction normal to the middle surface. A complex form of the resolvents of this theory, constructed in [6], is employed.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov. L'vov Franko State University. Translated from Mekhanika Polimerov, No. 6, pp. 1076–1081, November–December, 1970.     

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.     

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.     

Axisymmetric deformation of a thick circular glass-reinforced plastic cylinder with stiffening ribs

The state of stress of a circular glass-reinforced cylinder strengthened with equally spaced stiffening ribs has been investigated for uniform axisymmetric and longitudinal loads of intensity p. A system of equilibrium equations is obtained for the shell on the assumption that Hooke's law is valid and that the angles of rotation and shear are commensurable for deformation of an element of the structure. A solution of this system is given for boundary conditions that take into account the compatibility of strains of shell and ribs. As a result of an analysis of the solution the limits of applicability of the theory of thin shells to this type of structure are determined, the effect of anisotropy of the material is estimated, and recommendations are made regarding the choice of optimal reinforcing schemes for cylindrical shells.Mekhanika Polimerov, Vol. 2, No. 1, pp. 108–115, 1966     

Investigation of the performance of composite shells under repeat internal pressure

The effect of the winding material and its thickness on the residual strains and the mode of failure of a composite shell is analyzed. The results of low-cycle fatigue tests on composite shells are presented.P. I. Baranov Central Institute of Aircraft Engine Building. Translated from Mekhanika Polimerov, No. 6, pp. 1060–1065, November–December, 1973.     

Calculation of contact pressures in the cable pressing of a cylindrical plastic shell subjected to a nonstationary temperature field

Conclusions The use of internal heating in the manufacture of plastic shells by the cable-pressing method produces significantly higher compressing stresses in the shell, thus improving the quality of the material.Translated from Mekhanika Polimerov, No. 2, pp. 220–224, March–April, 1977.     

Optimization of cylindrical composite shells with regard to their critical mode of imperfections

This study deals with the optimum design of composite shells under external pressure with material strength and loss of stability according to the critical mode of imperfections taken as the failure criterion. The problem of optimum design is solved and the critical mode is obtained by nonlinear optimum programming for which the geometric and initial imperfection parameters are treated as variables. Numerical results are obtained for a cylindrical composite shell supported freely at its ends. The effect of shear forces between layers on the load-carrying capacity of the shell is also investigated.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 5, pp. 613–620, September–October, 1998.     

Deformation of momentless shells under internal pressure under conditions where the material undergoes creep

Relations are derived for the deformation of momentless shells under internal pressure and finite strains. The law governing the deformation of the material is assumed to be that for a typical, incompressible viscoelastic solid. The special cases of the behavior of a spherical shell under a constant internal pressure and for a constant amount of gas in the shell are solved. It is found that up to a given limit, at constant pressure the deformation of the shell falls off, while above this limit the deformation increases at an increasing rate. With a constant quantity of gas inside the shell the deformation again falls off, as far as initial application of an internal pressure to the shell, equal to the critical, elastic pressure.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1066–1072, November–December, 1972.     

Reaction of sloping spherical shells of glass-fiber-reinforced plastic during nonstationary loading

The behavior of spherical shells of glass-fiber-reinforced plastic under the action of exponentially changing dynamic loading was studied in a nonlinear formulation. The method of finite differences, used in the form of an explicit difference scheme, was used to solve the differential equations of the dynamics of sloping shells based on the Kirchhoff-Love hypotheses. The characteristic features of the deformation process and the influence of the degree of anistropy of the shell material operating under conditions of dynamic loading are noted.Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 311–314, March–April, 1975.     

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.     

Comparative analysis of two algorithms for numerical solution of nonlinearstatic problems for multilayered anisotropic shells of revolution 2. Account of transverse compression

Two algorithms for numerical solution of static problems for multilayer anisotropic shells of revolution are discussed. The first algorithm is based on a differential approach using the method of discrete orthogonalization, and the second one—on the finite element method with linear local approximation in the meridional direction. It is assumed that the layers of the shell are made of linearly elastic, anisotropic materials. As the unknown functions, six displacements of the shell are chosen, which often simplifies the definition of static problems for multilayer shells. The calculation of a cross-ply cylindrical shell stretched in the axial direction is considered. It is shown that taking account of the transverse compression, anisotropy, and geometrical nonlinearity is important for the given class of problems.Tambov State Technical University, Tambov, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 4, pp. 435–446, May–June, 1999.     

Estimation of the stability of the strength of glass-reinforced plastics in conical shells

On the basis of a statistical analysis of the test data it is shown that there is a difference between the mechanical characteristics (in tension and compression) of laminated glass-reinforced plastics obtained under laboratory and industrial conditions by impregnation under pressure in a closed mold. The stability of the strength properties of the glass-reinforced plastic in various conical shells, produced in large batches, is considered. Certain experimental relations between the material properties and the total number of shells produced are also established.Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 102–108, January–February, 1970.