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.

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.

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.

Distributed flexoelectric modal signals on circular cylindrical shells

2017 ◽  
Vol 232 (6) ◽  
pp. 952-961 ◽  
Author(s):  
Hua Li ◽  
Kaiming Hu ◽  
HS Tzou
Keyword(s):  
Strain Gradient ◽  
Cylindrical Shells ◽  
Mechanical Strain ◽  
Electric Polarization ◽  
Design Parameters ◽  
Flexoelectric Effect ◽  
Bending Strain ◽  
Longitudinal Bending ◽  
Circular Cylindrical Shells ◽  
Sensing Characteristics

Flexoelectricity exhibits both direct effect and converse effect. For direct flexoelectric effect, mechanical strain gradients induce a homogeneous electric polarization in dielectrics. Thus, the induced electric field between the electrodes can be measured. Compared with the piezoelectric sensors, the main advantage of the flexoelectric sensors is that they are not sensitive to the in-plane strains. This paper presents segmented flexoelectric sensors laminated on circular cylindrical shells, and investigates the electromechanical strain-gradient/signal-generation characteristics and distributed modal flexoelectric signals on the cylindrical shells. The dynamic equations of the proposed flexoelectric sensor are derived based on the direct flexoelectric effect and thin shell assumptions. The model of modal signal is derived to investigate the sensing characteristics. In case studies, the effects of design parameters, i.e. size and thickness of the sensors and geometry of the shells, are evaluated and compared. Numerical results indicate that the contribution of longitudinal bending strain gradient is dominant in the total signals of most evaluated modes, except that in modes 1 and 2, where the contribution of the circumferential bending strain gradient is slightly higher. The amplitudes of the modal signals decrease with the shell radius, but increase with the sensor thickness.

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.

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