Limit Point Buckling Loads of Axially Compressed, Circular Cylindrical Shells—The Effect of Nonlinear Material Behavior

1979 ◽  
Vol 46 (2) ◽  
pp. 386-392 ◽  
Author(s):  
R. P. Nimmer ◽  
J. Mayers
Keyword(s):  
Deformation Theory ◽  
Cylindrical Shells ◽  
Material Behavior ◽  
Nonlinear Material ◽  
Polyhedral Surface ◽  
Buckling Loads ◽  
Accurate Representation ◽  
Mechanism Model ◽  
Previously Treated ◽  
Circular Cylindrical Shells

The elasto-plastic buckling and postbuckling of imperfect, thin, circular cylindrical shells in axial compression is studied with the use of a mechanism model specifically designed to achieve an accurate representation of the developable polyhedral surface of Yoshimura. The formulation makes it possible to study the influence of asymmetric imperfection patterns of significantly larger amplitudes than previously treated. Elasto-plastic effects are included using a deformation theory of plasticity and Reissner’s variational principle. Material-sensitive load-shortening curves are obtained exhibiting initial-maximum values for the average axial stresses of imperfect shells that tend toward vanishingly small magnitudes with increasing radius-to-thickness ratio and attendant imperfections.

SCALING LAW AND PHYSICAL SIMILITUDE FOR BUCKLING AND VIBRATION OF ANTISYMMETRIC ANGLE-PLY LAMINATED CYLINDRICAL SHELLS

2003 ◽  
Vol 03 (04) ◽  
pp. 567-583 ◽  
Author(s):  
VARIDDHI UNGBHAKORN ◽  
PAIROD SINGHATANADGID
Keyword(s):  
Scaling Laws ◽  
Cylindrical Shells ◽  
Scaling Law ◽  
Stacking Sequence ◽  
Buckling Loads ◽  
Fundamental Frequencies ◽  
Numerical Studies ◽  
Yield Values ◽  
Circular Cylindrical Shells ◽  
Similitude Theory

The similitude invariants and scaling laws for the buckling and free vibration of antisymmetric angle-ply laminated circular cylindrical shells were derived by directly applying the similitude transformation to the governing differential equations of the problem considered. The scaling laws relate the buckling load and natural frequency of a model to those of a prototype when the similarity requirements between the two systems are fulfilled. In the absence of experimental data, the validity of the scaling laws was verified by calculating theoretically the buckling loads and fundamental frequencies of vibration of the model and substituting them into the scaling laws to yield values for the prototype, which were then compared with those directly computed for the prototype. The numerical studies show that for the case of complete similitude with various stacking sequence, number of plies, and radius ratio, the solutions predicted by the similitude theory agree exactly with those obtained directly from the theory. Some typical partial similitude cases were also investigated. It was demonstrated that the partial similitude model with distortion in stacking sequence is reliable for predicting the behavior of the prototype. On the other hand, models with distortion in material properties are not recommended because of the existence of large discrepancies in the predicted results.

STRUCTURAL SIMILITUDE AND SCALING LAWS OF ANTI-SYMMETRIC CROSS-PLY LAMINATED CYLINDRICAL SHELLS FOR BUCKLING AND VIBRATION EXPERIMENTS

2007 ◽  
Vol 07 (04) ◽  
pp. 609-627 ◽  
Author(s):  
VARIDDHI UNGBHAKORN ◽  
NUTTAWIT WATTANASAKULPONG
Keyword(s):  
Material Properties ◽  
Physical Modeling ◽  
Numerical Experiments ◽  
Scaling Laws ◽  
Cylindrical Shells ◽  
Buckling Loads ◽  
Closed Form Solutions ◽  
Fundamental Frequencies ◽  
Circular Cylindrical Shells ◽  
Predicted Values

Developed herein are the scaling laws for physical modeling of anti-symmetric cross-ply laminated circular cylindrical shells for buckling and free vibration experiments. In the absence of experimental data, the validity of the scaling laws is verified by numerical experiments. This is accomplished by calculating theoretically the buckling loads and fundamental frequencies of the model and substituting into the scaling laws to obtain the corresponding values of the prototype. The predicted values of the prototype from the scaling laws are then compared with existing closed-form solutions. Examples for the complete similitude cases with various stacking sequences, number of plies, and length-to-radius ratios show exact agreement. The derived relationships between the model and prototype will greatly facilitate and reduce the need for costly experiments. In reality, either due to the complexity of the scaling laws or to economize experimental cost and time, it may not be feasible to construct the model to fulfil the scaling laws completely. Thus, several possible models of partial similitude are investigated numerically. These include models with distortion in laminated material properties, stacking sequences and number of plies. Model with distortion in material properties yields a high percentage of discrepancy and is not recommended.

New Results for the Buckling Loads of Axially Compressed Cylindrical Shells Subject to Relaxed Boundary Conditions

1970 ◽  
Vol 37 (1) ◽  
pp. 93-100 ◽  
Author(s):  
J. G. Simmonds ◽  
D. A. Danielson
Keyword(s):  
Boundary Conditions ◽  
Large Range ◽  
Cylindrical Shells ◽  
Radius Ratio ◽  
Column Buckling ◽  
Buckling Loads ◽  
Circular Cylindrical Shells ◽  
Approach Zero ◽  
Range Of Values

A set of accurate buckling equations recently developed by the authors is used to compute the buckling loads of axially compressed circular cylindrical shells subject to “relaxed,” incremental boundary conditions. Over a large range of values of the length to radius ratio, L/R, the buckling loads are essentially 1/2 of the classical value, as has been found by many previous investigators using the simplified Donnell buckling equations. However, it is shown that as L/R → 0 or as L/R → ∞, the buckling loads approach zero, in contrast to the behavior predicted by the Donnell equations. The correct behavior as L/R → 0, first discovered by Koiter, may be interpreted as the buckling of a ring-beam constrained between two rigid, concentric, frictionless cylinders. The behavior as L/R → ∞ simply represents Euler column buckling.

scholarly journals Static Bending of Isotropic Circular Cylindrical Shells Based on the Higher Order Shear Deformation Theory of Reddy and Liu

2021 ◽  
Vol 26 (3) ◽  
pp. 141-162
Author(s):  
C.U. Nwoji ◽  
D.G. Ani ◽  
O.A. Oguaghamba ◽  
V.T. Ibeabuchi
Keyword(s):  
Shear Deformation ◽  
Displacement Field ◽  
Shell Length ◽  
Deformation Theory ◽  
Cylindrical Shells ◽  
Shear Deformation Theory ◽  
Radius Of Curvature ◽  
Continuous Increase ◽  
Bending Analysis ◽  
Circular Cylindrical Shells

Abstract In this paper, a displacement based shear deformation theory formulated on the cubic in-plane displacement field equation of Reddy and Liu is presented for the static bending analysis of isotropic circular cylindrical shells. The adopted displacement field accounts for a quadratic (parabolic) distribution of the transverse shear through the shell thickness as well as satisfies the need for a stress free upper and lower boundary surfaces of the shell. The equations of static equilibrium are obtained on application of the principle of virtual work. Numerical results of the bending analysis for the displacements and stresses are presented for the simply supported shell. A comparison made to those of the Kirchhoff-Love theory for varying shell length to mean – radius of curvature ratios, shows good agreement for thin shells irrespective of the shell length to radius of curvature ratio (l / a). The transverse sharing effect is found to be noticeable in the deformation of thick shells, however, this effect diminishes with a continuous increase in l / a ratios.

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