Buckling of Axially Compressed Circular Cylindrical Shells at Stresses Smaller Than the Classical Critical Value

1965 ◽  
Vol 32 (3) ◽  
pp. 542-546 ◽  
Author(s):  
N. J. Hoff ◽  
L. W. Rehfield
Keyword(s):  
Critical Stress ◽  
Cylindrical Shells ◽  
Bending Moment ◽  
Critical Value ◽  
Closed Form Solutions ◽  
Stress Resultant ◽  
Simple Support ◽  
Circumferential Displacement ◽  
Circular Cylindrical Shells ◽  
Support Conditions

Closed-form solutions are given of the linear Donnell equations defining the buckling of thin-walled circular cylindrical shells subjected to uniform axial compression. In addition to the classical simple support conditions requiring the vanishing of the radial displacement, the axial bending-moment resultant, the axial additional normal-stress resultant, and the circumferential displacement, three other, equally justifiable, simple support conditions are defined and studied in the case of the semi-infinite shell. Two of them yield buckling stresses amounting to about one half the classical critical stress.

Low Buckling Stresses of Axially Compressed Circular Cylindrical Shells of Finite Length

1965 ◽  
Vol 32 (3) ◽  
pp. 533-541 ◽  
Author(s):  
N. J. Hoff
Keyword(s):  
Normal Stress ◽  
Cylindrical Shells ◽  
Bending Moment ◽  
Critical Value ◽  
Stress Resultant ◽  
End Conditions ◽  
Simple Support ◽  
Longitudinal Bending ◽  
Circular Cylindrical Shells ◽  
Axial Normal Stress

Exact solutions are derived of the classical differential equations defining the deformations of axially compressed thin-walled circular cylindrical shells. The end conditions along the circular edges are assumed as the vanishing (a) of the radial displacement; (b) of the longitudinal bending moment; (c) of the variation in the axial normal stress resultant; and (d) of the circumferential membrane shear stress resultant. Under these conditions of simple support the critical value of the uniformly distributed axial normal stress is one half the classical critical value.

Investigation on the Influence of Stiffener Size on the Buckling Pressures of Circular Cylindrical Shells Under Hydrostatic Pressure

1962 ◽  
Vol 6 (03) ◽  
pp. 24-32
Author(s):  
James A. Nott
Keyword(s):  
Cylindrical Shells ◽  
High Strength ◽  
Plastic Buckling ◽  
Theoretical Derivation ◽  
Perfectly Plastic ◽  
Plastic Materials ◽  
Simple Support ◽  
Circular Cylindrical Shells ◽  
Support Conditions ◽  
Elastic Perfectly Plastic

A theoretical derivation is given for elastic and plastic buckling of stiffened, circular cylindrical shells under uniform external hydrostatic pressures. The theory accounts for variable shell stresses, as influenced by the circular stiffeners, and critical buckling pressures are obtained for simple support conditions at the shell-frame junctures. Collapse pressures for both elastic and plastic buckling are determined by iteration and numerical minimization. The theory is applicable to shells made either of strain-hardening or elastic-perfectly plastic materials. Using the developed analysis, it is shown that a variation in stiffener size can change the buckling pressures. Test data from high-strength steel and aluminum cylinders show agreement between the theoretical and experimental collapse pressures to within approximately six percent.

Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells Stiffened by a Bonded Central Shell Segment

2004 ◽  
Author(s):  
U. Yuceoglu ◽  
V. O¨zerciyes
Keyword(s):  
Cylindrical Shell ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Adhesive Layer ◽  
Shear Stresses ◽  
First Order ◽  
Stress Resultant ◽  
Circular Cylindrical Shells

This study is concerned with the “Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells Stiffened by a Bonded Central Shell Segment.” The base shell is made of an orthotropic “full” circular cylindrical shell reinforced and/or stiffened by an adhesively bonded dissimilar, orthotropic “full” circular cylindrical shell segment. The stiffening shell segment is located at the mid-center of the composite system. The theoretical analysis is based on the “Timoshenko-Mindlin-(and Reissner) Shell Theory” which is a “First Order Shear Deformation Shell Theory (FSDST).” Thus, in both “base (or lower) shell” and in the “upper shell” segment, the transverse shear deformations and the extensional, translational and the rotary moments of inertia are taken into account in the formulation. In the very thin and linearly elastic adhesive layer, the transverse normal and shear stresses are accounted for. The sets of the dynamic equations, stress-resultant-displacement equations for both shells and the in-between adhesive layer are combined and manipulated and are finally reduced into a ”Governing System of the First Order Ordinary Differential Equations” in the “state-vector” form. This system is integrated by the “Modified Transfer Matrix Method (with Chebyshev Polynomials).” Some asymmetric mode shapes and the corresponding natural frequencies showing the effect of the “hard” and the “soft” adhesive cases are presented. Also, the parametric study of the “overlap length” (or the bonded joint length) on the natural frequencies in several modes is considered and plotted.

On the Linear Buckling of Circular Cylindrical Shells Under Asymmetric Axial Compressive Stress Distributions

1966 ◽  
Vol 70 (672) ◽  
pp. 1095-1097 ◽  
Author(s):  
D. J. Johns
Keyword(s):  
Compressive Stress ◽  
Cylindrical Shells ◽  
Bending Moment ◽  
Transverse Load ◽  
Stress Distributions ◽  
Pure Bending ◽  
Linear Buckling ◽  
Circular Cylindrical Shells ◽  
Axial Compressive Stress

The linear buckling of circular cylindrical shells is considered with particular attention to the cantilever shell subjected to either a pure bending moment (M) or transverse load (P)—see Fig. 1. It is believed that the conclusions reached have wider application to more general loading cases.

Post-Buckling Behavior of Pressurized Long Circular Cylindrical Shells

1986 ◽  
Vol 30 (03) ◽  
pp. 172-176
Author(s):  
Charles W. Bert ◽  
Victor Birman
Keyword(s):  
Differential Equation ◽  
Cross Sections ◽  
Cylindrical Shells ◽  
Bending Moment ◽  
Global Behavior ◽  
Arbitrary Boundary ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Circular Cylindrical Shells ◽  
The Relationship

The problem of post-buckling behavior of long, vertical, circular cylindrical shells loaded by nonuniform pressure, tension, and their own weight is formulated in this paper. The global behavior is considered by assuming that local deformations do not influence the solution. The nonlinear effect is due to the softening of the relationship between the bending moment and curvature due to the effect of the flattening of the shell cross sections. The nonlinear differential equation obtained in this paper describes the post-buckling behavior of a shell with linearly distributed pressure along the axis and arbitrary boundary conditions. In the general case this problem must be solved numerically. An analytical solution is presented for a particular case of a shell loaded by a uniform external or internal pressure.

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.

Snapping of Imperfect Thin-Walled Circular Cylindrical Shells of Finite Length

1971 ◽  
Vol 38 (1) ◽  
pp. 162-171 ◽  
Author(s):  
K. Y. Narasimhan ◽  
N. J. Hoff
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Finite Length ◽  
Cylindrical Shells ◽  
Nonlinear Partial Differential Equations ◽  
Numerical Procedure ◽  
Maximal Load ◽  
Load Carrying ◽  
Circumferential Displacement ◽  
Circular Cylindrical Shells

The nonlinear partial differential equations of von Karman and Donnell governing the deformations of initially imperfect cylindrical shells are reduced to a consistent set of ordinary differential equations. A numerical procedure is then used to solve the equations together with the associated boundary conditions and to determine the number of waves at buckling as well as the load-carrying capacity of imperfect cylindrical shells of finite length subjected to uniform axial compression in the presence of a reduced restraint along the simply supported boundaries. It is found that details of the boundary conditions have little effect on the number of waves into which the shell buckles around the circumference. This number is determined essentially by the length-to-radius and radius-to-thickness ratios. The absence of an edge restraint to circumferential displacement reduces the classical value of the buckling load by a factor of about two. On the other hand, shells with these boundary conditions appear to be less sensitive to initial imperfections in the shape, and thus the maximal load supported in the presence of unavoidable initial deviations can be the same for shells with and without a restraint to circumferential displacements along the edges.

AXISYMMETRIC VIBRATION OF CYLINDRICAL SHELLS WITH INTERMEDIATE RING SUPPORTS

2003 ◽  
Vol 03 (01) ◽  
pp. 35-53
Author(s):  
Y. XIANG ◽  
C. W. LIM ◽  
S. KITIPORNCHAI
Keyword(s):  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Equation System ◽  
Axisymmetric Vibration ◽  
Decomposition Approach ◽  
New Exact Solutions ◽  
Intermediate Ring ◽  
Space Technique ◽  
Circular Cylindrical Shells ◽  
Support Conditions

This paper treats the axisymmetric vibration of thin circular cylindrical shells with intermediate ring supports based on the Goldenveizer–Novozhilov thin shell theory. An analytical method is proposed, and new exact solutions are presented to study the axisymmetric vibration characteristics of the ring supported cylindrical shells. In the proposed method, the state-space technique is employed to derive a homogenous differential equation system for a shell segment, and a domain decomposition approach is developed to cater for the continuity requirements between shell segments. Exact frequency parameters are presented for circular cylindrical shells that have multiple intermediate ring supports and various combinations of end support conditions. These exact vibration frequencies may serve as important benchmarks against which researchers can validate their numerical methods for such circular cylindrical shell problems.

The Ritz formulation applied to the study of the vibration frequency characteristics of functionally graded circular cylindrical shells

2009 ◽  
Vol 224 (1) ◽  
pp. 43-54 ◽  
Author(s):  
M N Naeem ◽  
S H Arshad ◽  
C B Sharma
Keyword(s):  
Vibration Frequency ◽  
Volume Fraction ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Frequency Spectra ◽  
Closed Form Solutions ◽  
Graded Material ◽  
Circular Cylindrical Shells ◽  
Direct Variational Method ◽  
Thin Shell Theory

In this article vibration frequencies of functionally graded circular cylindrical shells are analysed and studied using the Ritz formulation. Since closed-form solutions are limited to simple cases, an approximate method is employed to solve the shell problem, and numerical evaluation is carried out using a direct variational method. Axial modal dependence is chosen in terms of Ritz polynomials to ascertain a rapid convergence of the method. Sanders and Budiansky's thin shell theory is utilized for strain—displacement and curvature—displacement relations. Functionally graded material characteristics for the constituent materials are distributed in accordance with a volume fraction law. Influence of boundary conditions and volume fraction exponents on the vibration frequency spectra is analysed. The present results are compared with some previous works and excellent agreement is found.

Characteristic Equations in the Theory of Circular Cylindrical Shells

1962 ◽  
Vol 13 (1) ◽  
pp. 88-91 ◽  
Author(s):  
Ivar Holand
Keyword(s):  
Closed Form ◽  
Series Expansion ◽  
Characteristic Equation ◽  
Cylindrical Shells ◽  
Characteristic Equations ◽  
Closed Form Solutions ◽  
Circular Cylindrical Shells

SummaryClosed form solutions are given of the characteristic equation of the Hiigge theory with circumferential series expansion. Specialisations to simplified theories are shown.

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