Optimization of compressed cylindrical shells with elastic properties that vary along the length

An axially compressed orthotropic cylindrical shell, with modulus of elasticity that varies discretely or continuously along the length, is considered. The axisymmetric case is investigated. The optimal (in terms of weight) modulus of elasticity distribution is found, in the case of nonlinear mathematical programming, and then used to solve the optimal control problem.     

Buckling and the initial postbuckling behavior of cylindrical shells made of composites with one plane of symmetry

A method for calculating the buckling stability of layered cylindrical shells made of composite materials with one plane of symmetry of mechanical characteristics is worked out. As a special case, shells made of fibrous materials by winding in directions not coinciding with coordinate axes are considered. An analysis of stability of shells under an axial compression, external pressure, and torsion is carried out. It is shown that, at a great number of layers and appropriate reinforcing angles, the shells can be considered orthotropic. The solution to the problem of the initial postbuckling behavior of shells made of composites with one plane of symmetry is also obtained. It is found that shells of this type can be less sensitive to geometrical imperfections. This fact is important from the practical point of view. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 213–236, March–April, 2007.     

Mechanical behavior of cylindrical laminated plastic shells

The static and dynamic behavior of a cylindrical glass-reinforced plastic shell with an open cross section under long-term loading and unloading has been experimentally and theoretically investigated. The experimental results are compared with the theoretical data obtained using a geometrically nonlinear theory based on the Kirchhoff hypothesis. For calculation purposes the glass-reinforced plastic is assumed to be a homogeneous orthotropic linearly elastic material.Building Research Institute, Prague. Translated from Mekhanika Polimerov, No. 1, pp. 110–115, January–February, 1976.     

Experimental investigation of the stability of glass-reinforced plastic cylindrical shells subjected to long-term axial compression

The results of an experimental investigation of circular cylindrical glass-reinforced plastic shells under long-term axial compression are reported. The experimental method and the experimental apparatus are described. The initial irregularity functions and their evolution during loading and in time at various values of the compressive loads are investigated. The spread of the critical times at a given load level is studied together with the dependence of the critical time on the compressive load. The behavior of the shell after unloading and under alternating loading and unloading is considered. The correlation between the buckled shapes resulting from long-term compression and the initial irregularity functions is examined.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 4, pp. 710–713, July–August, 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.     

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.     

An investigation of the complete post-buckling behavior of axisymmetric spherical shells

Summary The post-buckling behavior of an elastic spherical shell is studied for large axisymmetric deformations. The complete post-buckling path is given for the experimentally confirmed single dimple solution in a load-deformation diagram, making use of the methods of local bifurcation theory, singular perturbation analysis and numerical analysis. From the specific form of the post-buckling path with its predominating unstable part follows the strong imperfection sensitivity of the shell structure.

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Zusammenfassung Es wird das Nachbeulverhalten einer elastischen Kugelschale für große achsensymmetrische Deformationen untersucht. Der gesamte Nachbeulpfad wird für die experimentell bestätigte single dimple Lösung, die eine starke lokale Eindellung darstellt, angegeben, wobei Methoden der lokalen Verzweigungstheorie, der singulären Störungsrechnung und der numerischen Analysis verwendet wurden. Aus der besonderen Form des Nachbeulpfades mit seinem überwiegend instabilen Teil ist die starke Imperfektionsempfindlichkeit dieser Konstruktion deutlich erkennbar.

     

Dynamic stability and sensitivity to geometric imperfections of strongly compressed circular cylindrical shells under dynamic axial loads

In the present paper, the dynamic stability of circular cylindrical shells is investigated; the combined effect of compressive static and periodic axial loads is considered. The Sanders–Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration; Lagrange equations are used to reduce the nonlinear partial differential equations to a set of ordinary differential equations. The dynamic stability is investigated using direct numerical simulation and a dichotomic algorithm to find the instability boundaries as the excitation frequency is varied; the effect of geometric imperfections is investigated in detail. The accuracy of the approach is checked by means of comparisons with the literature.     

On the investigation of free vibrations of nonthin cylindrical shells of variable thickness by the spline-collocation method

For determining the dynamic characteristics of free vibrations of circular unclosed cylindrical shells of variable thickness in two coordinate directions, we have used the spline-collocation method together with the method of discrete orthogonalization. The problem has been solved within the framework of the refined Timoshenko–Mindlin theory. We have also investigated the influence of different laws of change in the shell thickness on the character of its natural vibrations. Our calculations have been carried out for different geometrical and elastic parameters of the shell under study and different boundary conditions.     

Averaging of densely perforated cylindrical shells

Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 46, pp. 136–139, 1986.     

Stability of cylindrical glass-reinforced plastic shells

The stability of cylindrical shells in axial compression has been experimentally investigated. The glass-reinforced plastic shells were fabricated in various ways: by winding glass strand, from glass cloth, and by a combination of the first two methods. The buckling mode and critical load were determined as functions of the ratio of shell radius to shell thickness. A statistical analysis of the test data leads to a formula with an empirical coefficient for use in practical stability calculations.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 5, pp. 886–891, September–October, 1969.     

Sound insulation of composite cylindrical shells

We study problems involving the acoustic insulation of cylindrical shells of finite length made of a composite material. The motion of the medium (a gas) is described by the usual wave equation of acoustic approximation, and the equations of the applied theory of composite shells are used to describe the vibrations of the shell. To determine the levels of sound suppression the finite-element method is applied for both the medium and the shell. Translated fromMatematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 1, 1998, pp. 47–50.     

Experimental and theoretical study of the supporting power of longitudinally compressed slightly conical shells made of composite materials

Mechanics of Composite Materials -