Stability Of Orthotropic Cylindrical Shells Research Articles

Dynamic Stability of a Cylindrical Shell Reinforced by Longitudinal Ribs of Piecewise-Constant Thickness under Axial Loading

A model is proposed for studying the simultaneous parametric and longitudinal vibrations of an orthotropic cylindrical shell reinforced by longitudinal ribs of piecewise-constant thickness under the action of an axial time-harmonic load. The discrete location and changes in the thickness of the ribs are taken into account using generalized functions. The basic stages of solving the problem are considered with the combination of methods proposed. Using a numerical example, the dependences of the principal instability region on the geometric parameters of the ribs are plotted for the first time, and a comparison is made with the instability regions for the ribs with a mean-integral thickness. The model developed makes it possible to correct significantly the solutions of problems on calculation of the dynamic stability of orthotropic cylindrical shells with the ribs of piecewise-constant thickness.

Stability of Orthotropic Cylindrical Shells under Bending by a Transverse Force. Part 2. Experiment

The paper presents the results of an experimental study of the stability of orthotropic cylindrical shells in bending with a transverse force, which has been carried out on model shells. The peculiarities of the buckling process as a function of the parameters of shells are described. It has been shown that numerical solution with the aid of the LIRA software package, which is based on the linear stability theory, can be used to calculate the stability of elastic shells in transverse bending in the whole relative length range, which covers the “shear” and “flexural” forms of buckling, with an error of the order of 10%.

Stability of orthotropic cylindrical shells under bending by a transverse force. Part 1. Theory

Using the LIRA software package, we study the stability problem of isotropic and orthotropic cylindrical shells subjected to bending by a transverse end force. The parametrical analysis of the solution obtained is performed and the accuracy of available approximate estimates of the critical force value is evaluated.

On stability of orthotropic cylindrical shells

In contrast to [1–3], the present paper obtains a system of stability equations and the corresponding resolving equation for orthotropic cylindrical shells of any but very short length in the case where the precritical stress state cannot be treated as the zero-moment state. These equations are a generalization of the results obtained in [4]. On the basis of these equations, one can obtain both the well-known formulas [1–3] and, for medium-length shells, some new expressions of the critical load in longitudinal compression and that under the joint action of torsionalmoments, normal pressure, and longitudinal compression. Some estimates are performed and the determination of the domain of application of some formulas given in [2] and in the present paper is attempted. For an orthotropic shell, a relationship between the elastic parameters and the shear modulus is established for axisymmetric and nonaxisymmetric buckling mode shapes in longitudinal compression.

The Dynamic Stability of Orthotropic Cylindrical Shells with Non-homogenous Material Properties under Axial Compressive Load Varying as a Parabolic Function of Time

In this study, the dynamic stability problem of a cylindrical shell composed of non-homogeneous orthotropic materials with Young’s moduli and density varying continuously in the thickness direction under the effect of an axial compressive load varying with a parabolic function of time is considered. At first, the fundamental relations and the modified Donnell type dynamic stability equations of a non-homogeneous orthotropic cylindrical shell are set up. Applying the Galerkin method, first, and then the Ritz-type variational method, the closed-form solutions have been derived for the dynamic critical axial load and dynamic factor. Finally, carrying out some computations, the effects of the non-homogeneity of the orthotropy ratio and the axial loading parameter on the critical parameters have been studied. Comparing results with those in the literature validates the present analysis.

Effect of lamination of the material on the stability of orthotropic cylindrical shells

Effect of lamination of the material on the stability of orthotropic cylindrical shells

Stability of orthotropic cylindrical shells under combined loading

Stability of orthotropic cylindrical shells under combined loading

Investigation of stability of orthotropic cylindrical shells with a filter

Investigation of stability of orthotropic cylindrical shells with a filter

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.

Long-time stability of orthotropic cylindrical shells under external pressure

The problem is solved using a refined theory of shells that takes shear strains into account. The shell deformations are described by means of the relations for an orthotropic material, it being assumed that creep strains develop only as a result of shear forces. The geometrically linear problem is considered. For the sake of comparison, the long-time critical load is calculated on a Minsk-22 computer using the Kirchhoff-Love and refined models. It is shown that when shears are taken into account, in certain cases the critical load may be reduced by 30%.

Influence of boundary conditions and elastic characteristics of the stability of orthotropic cylindrical shells

Influence of boundary conditions and elastic characteristics of the stability of orthotropic cylindrical shells

Stability of orthotropic cylindrical shells with considerations of the moments affecting the subcritical state

Stability of orthotropic cylindrical shells with considerations of the moments affecting the subcritical state

SOME RECENT CONTRIBUTIONS TO PANEL FLUTTER RESEARCH

5 Donnell, L. EL, of thin-walled tubes under torsion, NACA Kept. 479, pp. 95-115 (1934). 6 Flugge, W., Stresses in Shells (Springer-Verlag, Berlin, 1962). 7 Green, A. and Zerna, W., Theoretical Elasticity (Oxford University Press, London, 1954). 8 Gerard, G. and Becker, H., Handbook of structural stability, Part III—Buckling of curved plates and shells, NACA TN 3783 (August 1957). 9 Hess, T. E., of orthotropic cylindrical shells under combined loading, ARS J. 31, 237-246 (1961). 10 Timoshenko, S. and Gere, J., Theory of Elastic Stability (McGraw-Hill Book Co. Inc., New York, 1961). 11 Love, A. E., A Treatise on the Mathematical Theory of Elasticity (Dover Publications, New York, 1944). 12 March, H. W., Norris, C. B., Smith, C. B., and Kuenzi, E. W., Buckling of thin-walled plywood cylinders in torsion, Forest Products Lab. Rept. 1529 (June 1945). 13 March, H. W., Buckling of long, thin plywood cylinders in axial compression, Forest Products Lab. Rept. 1322-A (March 1956). 14 Novozhilov, V. V., Theory of Thin Shells (P. Noordhoff Ltd., Groningen, Netherlands, 1959). 15 Von Karman, T. and Tsien, H. S., The buckling of thin cylindrical shells under axial compression, J. Aeronaut. Sci. 8,303-312(1941). 16 Ho, B. P. C. and Cheng, S., Some problems in stability of heterogeneous aeolotropic cylindrical shells under combined loading, AIAA J. (to be published).

Stability of Orthotropic Cylindrical Shells Under Combined Loading

N THE design of modern missiles and space vehicles, in­ creasing use is made of the newer materials, such as rein­ forced plastics, whisker materials and fiber reinforced metals. Materials of this sort are elastically orthotropic; that is, they have three mutually perpendicular planes of elastic symmetry. This means that the material composing the wall of a shell has a modulus of elasticity and Poisson's ratio different in the axial than in the circumferential direction, and a shear modulus which is completely independent of these. The critical item in the design of structures utilizing these materials may be stability, depending on the strength, duc­ tility and stiffness of the material. If such is the case, a method of predicting the buckling load is required. One possibility is to use an isotropic analysis such as given in (l), 2 assuming some average material properties. However, this approach could lead to results that would be unduly conserva­ tive in some cases, and disastrously nonconservative in other cases. Therefore, the purpose of this report is to present a method of determining the buckling loads on shells composed of an orthotropic material. In this report the small deflection differential equations describing the action of an orthotropic cylindrical shell under arbitrary loading are derived. These equations are then transformed into the large deflection equations effectively, describing the stability of the shell under the action of ex­ ternal pressure and axial compression (2). The solution of the latter equations yields an expression for the critical loads in terms of shell geometry, material properties and buckling modes. There is an infinite number of possible buckling modes but the only one of practical interest is the one cor­ responding to minimum load. A family of curves is plotted giving the critical axial load and critical external pressure for an orthotropic cylinder. For a conical shell of small vertex angle, the equivalent cylinder method developed by Bijlaard (7) and discussed in (1) is recommended.