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.     

Effect of prestress on the strength of metal shells reinforced with a glass-reinforced plastic

The effect of prestress on the strength of metal glass-reinforced plastic shells has been investigated. A method of calculation is described, and experimental results showing the role of the tensile stress in the reinforcement of reinforced metal shells are presented.Mekhanika Polimerov, Vol. 2, No. 2, pp. 285–289, 1966     

Vibration analysis of truncated conical shells subjected to flowing fluid

A method to predict the dynamic behaviour of anisotropic truncated conical shells conveying fluid is presented in this paper. It is a combination of finite element method and classical shell theory. The displacement functions are derived from exact solutions of Sanders’ shell equilibrium equations of conical shells. The velocity potential, Bernoulli’s equation and impermeability condition have been applied to the shell–fluid interface to obtain an explicit expression for fluid pressure which yields three forces (inertial, centrifugal, Coriolis) of the moving fluid. To the best of the authors’ knowledge, this paper reports the first comparison made between two works which deal with conical shells subjected to internal flowing fluid effects. The results obtained by this method for conical shells with various boundary condition and geometries, in vacuum, fully-filled and when subjected to flowing fluid were compared with those of other experimental and numerical investigations and good agreement was obtained.     

A direct method for determining the mass of gases in ICF shell

In the present paper, the defects of dew point method for measuring the mass of gas filled in ICF shells are analyzed. An accurate state equation for gas D2 is deduced from Benedict-Webb-Rubin (BWR) equation and experimental data in planar phase. A direct method to determine gas mass in ICF shells via measuring the temperature and pressure outside the shells and solving the equation of state by numerical method is proposed. It overcomes the theoretical defects of dew point method and the complexities of equipment. In the present method, the state equation can be improved by more accurately measuring P-V-T values of gas D2, so the measuring precision of the mass of gas in the shells can also be improved. The present method is effective for treating mix gases filled in the shells as well. The errors between the computational results and experimental data are very small. Some cases in the filling process are predicted, and the proper temperature and pressure for filling gases effectively are also suggested.     

多层复合材料圆柱壳的非线性失稳计算

本文用能量法和有限差分法分析了多层复合材料圆柱壳在轴压、静水压力及扭转等载荷作用下的非线性屈曲和后屈曲性能。本文考虑了柱壳的初始缺陷、几何非线性、材料的物理非线性(剪切模量非线性)等因素对于临界载荷的影响。同时还讨论了横向剪切效应。计算分析结果与一些实验结果比较一致。     

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.     

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.     

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.     

Effect of Holes on the Eigenmodes of Reinforced Shells of Rotation

The vibrational eigenmodes of reinforced shells of rotation with holes are examined. A solution is constructed on the basis of the linear theory of thin elastic shells using the Ritz method. Results are presented from numerical studies of the effect of holes and reinforcements on the eigenmodes and forms of the vibrations. The results are compared with experimental data.     

Theoretical-experimental investigation of frequencies of free vibrations of circular cylindrical shells

We consider a holographic interferometry technique for the determination of frequencies of free vibrations of isotropic circular cylindrical shells and compare the experimental results with results of calculation of frequencies of these shells on the basis of the spline collocation technique.     

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 unfigured and stiffened shells made of fibrous composites

Conclusions Within the known generalizations of the theory of thin shells, formulas were obtained for calculating critical loads of unfigured and stiffened cylindrical shells made of fibrous composite materials under an external pressure and axial compression, taking into account not only the longitudinal (compressive) and flexural rigidity, but also the torsional and shear rigidities. From an analysis of the testing results of unfigured shells made of fiber-glass material, the divergence between the calculated and experimental data has been estimated by introducing into the formulas correction functions 0.181 In + 1.32 and a coefficient 0.697. The values of the safety factor were determined, which with a given reliability guarantee the selection of the geometrical parameters of the shells, amounting to (for a 0.95 reliability) 1.244 and 1.45.Paper presented at the Fourth All-Union Conference on the Mechanics of Polymer and Composite Materials (Riga, October, 1980).Translated from Mekhanika Kompozitnykh Materialov, No. 4, pp. 640–646, July–August, 1980.     

Some problems in the application of statistical dynamics to shells manufactured from fibrous composites

On the basis of a statistical approach presupposing direct utilization of experimental data produced in modelling operations, a procedure is proposed for computational estimates on composite materials in which allowance is made for the initial defects, the variable properties of the material, and the conditions of use (physical medium). Experimental data on Plexiglas shells which confirm the practical applicability of the procedure are given. Questions relating to the design of tests on composite shells are discussed.Translated from Mekhanika Polimerov, No. 4, pp. 743–745, July–August, 1972.     

Statistical analysis of some characteristics of cylindrical glass-fiber-reinforced plastic materials

The results are given of a statistical treatment of experimental data on several characteristics of glass-fiber-reinforced plastic cylindrical shells, prepared from glass fabric TS8/3-250 and epoxide binder IF-ÉD-6 (TU-26-59) at the "Électroizolit" factory by winding an impregnated fabric cloth on a mandrel. The experim ental data on the mechanical properties of the glass-fiber-reinforced plastic material were obtained in tests on representative samples cut from the margin of the cylindrical shells. The results of the statistical analysis can be used to evaluate the mechanical reliability of structures made of glass-fiber-reinforced plastic material of the above type.Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 906–910, September–October, 1973.     

Investigation of the initial imperfections and buckling modes of glass-reinforced plastic shells under hydrostatic pressure

The results of testing the stability of glass-reinforced plastic cylindrical shells under hydrostatic pressure are examined. The initial imperfections and deflections of the shells were directly measured. It is found that during loading or in the course of time (under load) the shape of the initial imperfections is transformed. An algorithm (see [11]) based on the approximation of the experimental deflection function by a Fourier series is used to establish the characteristic coefficients of the series important in connection with the elastic loss of stability and progressive buckling of the shell.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1057–1063, November–December, 1971.     

圆柱薄壳在外压作用下屈曲的边界层理论

本文依据文[14]提供的圆柱薄壳屈曲的边界层理论,以挠度为摄动参数,采用奇异摄动方法,研究了固支圆柱薄壳在侧向外压和静水外压作用下的屈曲和后屈曲性态.本文同时考虑了初始几何缺陷的影响.计算结果与实验结果的比较表明二者是一致的.     

Initial imperfections and buckling modes of polymeric cylindrical shells under long-term loading

The problem of buckling of polymeric cylindrical shells under long-term loading is considered. The results of compressive and external-pressure tests on shells [10, 11, 12, 17] are discussed and their carrying capacity is estimated [16]. The buckling problem is solved theoretically on the basis of an investigation of the development of axisymmetric modes and their conversion to nonaxisymmetric modes [15]. The equations of the nonlinear theory of viscoelasticity are used as the physical relations. The theoretical model gives qualitative agreement with the experimental behavior of the shell under load.     

Buckling shapes and hypercritical stressed state of viscoelastic shells

The buckling of shells of various thicknesses made from materials subject to nonlinear creep was studied experimentally. The distribution of the characteristic buckling shapes was established by spectral [harmonic] analysis. On the basis of the fundamental cubic theory of viscoelasticity [7], relationships are derived for determining the stress tensor components from the experimental deflection functions, with due allowance for various time factors. The stressed state of the test shells is analyzed. In approximating the deflection and stress functions use is made of a Fourier series in complex form.     

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.     

The non-linear deformation and stability of elliptical cylindrical shells under transverse bending

A finite-element formulation of the solution of problems of the stability of non-circular cylindrical shells taking into account their bending moments and the non-linearity of their precritical stress-strain state in proposed. Explicit expressions for the displacements of the elements of non-circular cylindrical shells as rigid bodies are derived by integration of the equations obtained by equating the components of the linear strains to zero. These expressions are used to construct shape functions of an effective quadrilateral finite element of the natural curvature. An effective algorithm is developed for investigating the non-linear deformation and stability of the shells. The stability of a cylindrical shell of elliptical cross-section under transverse bending is investigated. The influence of the ellipticity and non-linearity of the deformation on the shell's stability is determined. The results of the analysis are compared with experimental data.