Buckling of axially compressed cylindrical shells with local imperfections

Buckling of circular cylindrical shells in axial compression buckling of circular cylindrical shells in axial compression. buckling of circular cylindrical shells in axial compression

Buckling of cracked cylindrical thin shells under combined internal pressure and axial compression

Cylindrical shells under uniaxial compression and spherical shells under equi-biaxial compression display the most extreme buckling sensitivity to imperfections. In engineering practice, the reduction of load carrying capacity due to imperfections is usually addressed by use of a knockdown factor to lower the critical buckling stress estimated or computed without accounting for imperfections. For thin elastic cylindrical shells under uniaxial compression and spherical shells under equi-biaxial compression, the knockdown factor is typically as small as 0.2. This paper explores the alleviation of imperfection-sensitivity for loadings with a reduced circumferential (transverse) membrane stress component. The analysis of Koiter (1963) on the effect of an axisymmetric imperfection on the elastic buckling of a cylindrical shell under uniaxial compression is extended to both cylinders and spheres for loadings that produce general combinations of biaxial membrane stresses. Increases in the knockdown factor due to a reduction of the transverse membrane component are remarkably similar for cylindrical and spherical shells.

An analytical model is presented to predict the influence of nonlinearities associated with supersonic fluid flow on the dynamic and stability behavior of thin isotropic cylindrical shells. The method developed is a combination between finite element method, sander’s shell theory and nonlinear aerodynamic theory (third-order piston theory). The shell is subdivided into cylindrical finite elements, the displacements functions are derived from exact solutions of Sanders equations for thin cylindrical shells and the influence of stress stiffening due to internal or external pressure and axial compression is also taken into account. Expressions for the masse and stiffness matrices are determined by exact analytical integration. With the nonlinear dynamic pressure, we develop nonlinear matrices: stiffness, damping and coupling matrices for flow. The nonlinear equation of motion is then solved using a fourth-order Runge-kutta numerical method. Frequency variations are determined with respect to the amplitude of the motion for different cases. This is a powerful model to predict linear, nonlinear vibrations and stability characteristics of cylindrical shells subjected to external supersonic flow that can be applied for the aeroelastic design of aerospace vehicles.

The results of an analytical study of the nonlinear response of a thin unstiffened aluminum cylindrical shell with a longitudinal crack are presented. The shell is analyzed with a nonlinear shell analysis code that maintains the shell in a nonlinear equilibrium state while the crack is grown. The analysis accurately accounts for global and local structural response phenomena. Results are presented for internal pressure, axial compression, and combined internal pressure and axial compression loads. The effects of varying crack length on the nonlinear response of the shell subjected to internal pressure are described. The effects of varying crack length on the prebuckling, buckling and postbuclking responses of the shell subjected to axial compression, and subjected to combined internal pressure and axial compression are also described. The results indicate that the nonlinear interaction between the in-plane stress results and the out-of-plane displacements near a crack can significantly affect the structural response of the shell. The results also indicate that crack growth instabilities and shell buckling instabilities can both affect the response of the shell as the crack length is increased.

Stability analysis of a cylindrical shell with axially symmetric defects under axial compression based on the reduction stiffness method

Generally, thin cylindrical shells are susceptible for geometrical imperfections like non-circularity, non-cylindricity, dents, swellings etc. All these geometrical imperfections decrease the static buckling strength of thin cylindrical shells, but in this paper only effect of a dent on strength of a short (L / D ∼1 and R/t = 280) stainless steel cylindrical shell is considered for analysis. The dent is modeled on the FE surface of perfect cylindrical shell for different angles of inclination and sizes at half the height of cylindrical shell. The cylindrical shells with a dent are analyzed using non-linear static buckling analysis. From the results it is found that in case of shorter dents, size and angle of inclination dents do not have much effect on static buckling strength of thin cylindrical shells, where as in the case of long dents, size and angle of inclination of dents have significant effect. But both short and long dents reduce the static buckling strength drastically.

Nonsymmetric buckle patterns in progressive plastic buckling

Buckling of thin cylindrical shells: an attempt to resolve a paradox

The two-dimensional problem of plane sound wave impulse scattering on the thin elastic circular cylindrical shell cracked along its infinite length. The shell is empty inside and surrounded by water from outside. The Kirchhoff - Love theory for description of elastic shell dynamic equilibrium is used. The shell defect influence on the echo-signal structure is investidated.

This chapter is devoted to the stability behavior of thin cylindrical shells. The basic governing equations of thin circular cylindrical shells employing the Donnell theory with the von-Karman geometrical non-linearity are derived. The nonlinear strain-displacement relations, the nonlinear equilibrium equations, and the linear stability equations are derived employing the variational formulations. The cylindrical shell under uniform compressive axial load is considered and the buckling load is obtained and given by closed form solution. Thermal buckling of cylindrical shell made of FGM for the uniform temperature rise, linear radial temperature, and the nonlinear radial temperature are presented and the effect of piezo-control is examined. Buckling and postbuckling of thin cylindrical shells with piezo-control under thermal loads is discussed and the chapter concludes with the stability discussion of cylindrical shells on elastic foundation. The buckling loads of cylindrical shells of isotropic/homogeneous material are derived by simply setting proper values for the power law index of the FG materials.

Multiple geometric defects: Their effect on stability of cylindrical shells

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).

A theory of thin multilayer anisotropic viscoelastic cylindrical shells with allowance for quasistatic oscillations, based on the application of asymptotic analysis of small geometric parameters to the general three-dimensional equations of the viscoelasticity theory for curvilinear coordinates, is proposed. Recurrent sequences of local problems of the viscoelasticity theory for shells under the quasistatic pressure oscillations are formulated and analytical solutions are obtained. It is shown that with this approach it is possible to obtain expressions for all 6 components of the stress tensor over the thickness of the shell. An example of the calculation of a cylindrical viscoelastic shell with axisymmetric bending with allowance for quasistatic oscillations is considered. The graphs of the dependences of the components of the stress tensor on the local coordinate are given for different angles of layers in the material. An algorithm is proposed for obtaining explicit analytical equations for calculating the distribution of the total stress tensor components over a cylindrical shell under the action of quasistatic oscillations.

This article describes the use of fibre reinforced polymer composites to increase the strength of an isotropic metallic cylindrical shell against elephant’s foot buckling. This form of buckling occurs when a cylindrical shell structure is subjected to high internal pressure together with an axial force, such as those that may occur in tanks and silos. It is particularly relevant to tanks under seismic action. Although fibre reinforced polymer composites have been widely applied to different types of structures under several loading conditions, its use to strengthen thin steel cylindrical shells has been very limited. Here, a non-linear elasto-plastic finite element idealisation is used to explore the strengthening effect of a fibre reinforced polymer strip on a thin cylinder. The optimum size and position of the fibre reinforced polymer sheet were obtained and empirically formulated. This study has shown that the strength after repair is sensitive to minor changes in the fibre reinforced polymer parameters so that a close adherence to the optimum parameter values is very desirable.