Buckling of Thick Orthotropic Cylindrical Shells Under External Pressure

1993 ◽  
Vol 60 (1) ◽  
pp. 195-202 ◽  
Author(s):  
G. A. Kardomateas
Keyword(s):  
Critical Load ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Three Dimensional ◽  
Stability Loss ◽  
External Pressure ◽  
Elasticity Solution ◽  
Composite Shells

An elasticity solution to the problem of buckling of orthotropic cylindrical shells subjected to external pressure is presented. In this context, the structure is considered a three-dimensional body. The results show that the shell theory predictions can produce nonconservative results on the critical load of composite shells with moderately thick construction. The solution provides a means of accurately assessing the limitations of shell theories in predicting stability loss.

Buckling of Long Sandwich Cylindrical Shells Under External Pressure

2004 ◽  
Vol 72 (4) ◽  
pp. 493-499 ◽  
Author(s):  
G. A. Kardomateas ◽  
G. J. Simitses
Keyword(s):  
Transverse Shear ◽  
Shell Thickness ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Three Dimensional ◽  
Stability Loss ◽  
External Pressure ◽  
Composite Construction ◽  
The Core ◽  
Sandwich Construction

An elasticity solution to the problem of buckling of sandwich long cylindrical shells subjected to external pressure is presented. In this context, the structure is considered a three-dimensional body. All constituent phases of the sandwich structure, i.e., the facings and the core, are assumed to be orthotropic. The loading is a uniform hydrostatic pressure, which means that the loading remains normal to the deflected surface during the buckling process. Results are produced for laminated facings, namely, boron/epoxy, graphite/epoxy and kevlar/epoxy laminates with 0deg orientation with respect to the hoop direction, and for alloy-foam core. Shell theory results are generated with and without accounting for the transverse shear effect. Two transverse shear correction approaches are compared, one based only on the core, and the other based on an effective shear modulus that includes the face sheets. The results show that the shell theory predictions without transverse shear can produce highly non-conservative results on the critical pressure, but the shell theory formulas with transverse shear correction produce reasonable results with the shear correction based on the core only being in general conservative (i.e., critical load below the elasticity value). The results are presented for four mean radius over shell thickness ratios, namely 15, 30, 60, and 120 in order to assess the effect of shell thickness (and hence that of transverse shear). For the same thickness, the differences between elasticity and shell theory predictions become larger as the mean radius over thickness ratio is decreased. A comparison is also provided for the same shell with homogeneous composite construction. It is shown that the sandwich construction shows much larger differences between elasticity and shell theory predictions than the homogeneous composite construction. The solution presented herein provides a means of a benchmark for accurately assessing the limitations of shell theories in predicting stability loss in sandwich shells.

Bifurcation of Equilibrium in Thick Orthotropic Cylindrical Shells Under Axial Compression

1995 ◽  
Vol 62 (1) ◽  
pp. 43-52 ◽  
Author(s):  
G. A. Kardomateas
Keyword(s):  
Axial Compression ◽  
Orthotropic Material ◽  
Shell Theory ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Elasticity Solution ◽  
Timoshenko Theory ◽  
Cylinder Axis ◽  
Dimensional Theory ◽  
Nonshallow Shell

The bifurcation of equilibrium of an orthotropic thick cylindrical shell under axial compression is studied by an appropriate formulation based on the three-dimensional theory of elasticity. The results from this elasticity solution are compared with the critical loads predicted by the orthotropic Donnell and Timoshenko nonshallow shell formulations. As an example, the cases of an orthotropic material with stiffness constants typical of glass/epoxy and the reinforcing direction along the periphery or along the cylinder axis are considered. The bifurcation points from the Timoshenko formulation are always found to be closer to the elasticity predictions than the ones from the Donnell formulation. For both the orthotropic material cases and the isotropic one, the Timoshenko bifurcation point is lower than the elasticity one, which means that the Timoshenko formulation is conservative. The opposite is true for the Donnell shell theory, i.e., it predicts a critical load higher than the elasticity solution and therefore it is nonconservative. The degree of conservatism of the Timoshenko theory generally increases for thicker shells. Likewise, the Donnell theory becomes in general more nonconservative with thicker construction.

Approximate Elasticity Solution for Orthotopic Cylinder Under Hydrostatic Pressure and Band Loads

1970 ◽  
Vol 37 (1) ◽  
pp. 101-108 ◽  
Author(s):  
A. P. Misovec ◽  
J. Kempner
Keyword(s):  
Approximate Solution ◽  
Shell Theory ◽  
Good Accuracy ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
External Pressure ◽  
Theory Of Elasticity ◽  
Numerical Comparison ◽  
Axial Loads ◽  
Special Case

An approximate solution to the Navier equations of the three-dimensional theory of elasticity for an axisymmetric orthotopic circular cylinder subjected to internal and external pressure, axial loads, and closely spaced periodic radial loads is developed. Numerical comparison with the exact solution for the special case of a transversely isotropic cylinder subjected to periodic band loads shows that very good accuracy is obtainable. When the results of the approximate solution are compared with previously obtained results of a Flu¨gge-type shell solution of a ring-reinforced orthotropic cylinder, it is found that the shell theory gives fairly accurate representations of the deformations and stresses except in the neighborhood of discontinuous loads. The addition of transverse shear deformations does not improve the accuracy of the shell solution.

The Strength-Instability Interaction of Double-Skinned Composite Circular Shells under External Pressure

1984 ◽  
Vol 198 (4) ◽  
pp. 293-301 ◽  
Author(s):  
T Nash ◽  
P Montague
Keyword(s):  
Lower Bound ◽  
Epoxy Resin ◽  
Empirical Evidence ◽  
Cylindrical Shells ◽  
External Pressure ◽  
Composite Shells ◽  
Pressure Testing ◽  
Thin Steel ◽  
Type Interaction ◽  
Experimental Behaviour

This paper describes the construction and external pressure-testing of cylindrical shells fabricated by filling the annulus between two thin steel concentric membranes with an epoxy resin-glass syntatic foam. The investigation was specifically aimed to study the strength-instability interaction of relatively thin composite shells. The experimental behaviour of eight shells is reported and their failure pressures are compared with previously published predictions. The results provided empirical evidence to support a modified Rankine-type interaction curve yielding safe lower bound solutions.

Stability Loss in Thick Transversely Isotropic Cylindrical Shells Under Axial Compression

1993 ◽  
Vol 60 (2) ◽  
pp. 506-513 ◽  
Author(s):  
G. A. Kardomateas
Keyword(s):  
Axial Compression ◽  
Critical Loads ◽  
Shell Theory ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Stability Loss ◽  
Theory Of Elasticity ◽  
Dimensional Theory ◽  
Perfect Agreement ◽  
The Stability

The stability of equilibrium of a transversely isotropic thick cylindrical shell under axial compression is investigated. The problem is treated by making appropriate use of the three-dimensional theory of elasticity. The results are compared with the critical loads furnished by classical shell theories. For the isotropic material cases considered, the elasticity approach predicts a lower critical load than the shell theories, the percentage reduction being larger with increasing thickness. However, both the Flu¨gge and Danielson and Simmonds theories predict critical loads much closer to the elasticity value than the Donnell theory. Moreover, the values of n, m (number of circumferential waves and number of axial half-waves, respectively, at the critical point) for both the elasticity, and the Flu¨gge and the Danielson and Simmonds theories, show perfect agreement, unlike the Donnell shell theory.

A Finite-Deformation Shell Theory for Carbon Nanotubes Based on the Interatomic Potential—Part II: Instability Analysis

2008 ◽  
Vol 75 (6) ◽  
Author(s):  
J. Wu ◽  
K. C. Hwang ◽  
J. Song ◽  
Y. Huang
Keyword(s):  
Carbon Nanotubes ◽  
Internal Pressure ◽  
Critical Load ◽  
Finite Deformation ◽  
Shell Theory ◽  
Interatomic Potential ◽  
External Pressure ◽  
External Pressures ◽  
Tension And Compression ◽  
Potential Part

Based on the finite-deformation shell theory for carbon nanotubes established from the interatomic potential in Part I of this paper, we have studied the instability of carbon nanotubes subjected to different loadings (tension, compression, internal and external pressures, and torsion). Similar to the conventional shells, carbon nanotubes may undergo bifurcation under compression/torsion/external pressure. Our analysis, however, shows that carbon nanotubes may also undergo bifurcation in tension and internal pressure, though the bifurcation modes for tension and compression are very different, and so are the modes for the internal and external pressures. The critical load for instability and bifurcation depends on the interatomic potential used.

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