On the Buckling of Circular Cylindrical Shells Under Pure Bending

1961 ◽  
Vol 28 (1) ◽  
pp. 112-116 ◽  
Author(s):  
Paul Seide ◽  
V. I. Weingarten
Keyword(s):  
Galerkin Method ◽  
Compressive Stress ◽  
Cylindrical Shells ◽  
Bending Stress ◽  
Pure Bending ◽  
Circular Cylindrical Shells ◽  
The Stability ◽  
The Galerkin Method

The stability of circular cylindrical shells under pure bending is investigated by means of Batdorf’s modified Donnell’s equation and the Galerkin method. The results of this investigation have shown that, contrary to the commonly accepted value, the maximum critical bending stress is for all practical purposes equal to the critical compressive stress.

scholarly journals Vibration of rotating circular cylindrical shells with distributed springs

2021 ◽  
Vol 37 ◽  
pp. 346-358
Author(s):  
Fuchun Yang ◽  
Xiaofeng Jiang ◽  
Fuxin Du
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Shell Theory ◽  
Rotation Speed ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Governing Equations ◽  
Natural Response ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

Abstract Free vibrations of rotating cylindrical shells with distributed springs were studied. Based on the Flügge shell theory, the governing equations of rotating cylindrical shells with distributed springs were derived under typical boundary conditions. Multicomponent modal functions were used to satisfy the distributed springs around the circumference. The natural responses were analyzed using the Galerkin method. The effects of parameters, rotation speed, stiffness, and ratios of thickness/radius and length/radius, on natural response were also examined.

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.

Effects of Elastic Supports on the Buckling of Circular Cylindrical Shells Under Bending

1980 ◽  
Vol 47 (4) ◽  
pp. 866-870 ◽  
Author(s):  
T. Yabuta
Keyword(s):  
Galerkin Method ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
Elastic Support ◽  
Spring Constant ◽  
Elastic Supports ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

This paper presents the effects of elastic supports on the buckling of circular cylindrical shells under bending. Stability was investigated using Donnell’s equation and the Galerkin method, including the spring constant of the elastic support. The results of this investigation indicate that the effects are similar in the cases of bending and axial compression.

Buckling of Circular Cylindrical Shells Using a Displacement Function

1974 ◽  
Vol 96 (4) ◽  
pp. 1322-1327
Author(s):  
Shun Cheng ◽  
C. K. Chang
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
External Pressure ◽  
Displacement Function ◽  
Combined Loading ◽  
Trial Solution ◽  
Governing Differential Equation ◽  
Circular Cylindrical Shells ◽  
The Stability

The buckling problem of circular cylindrical shells under axial compression, external pressure, and torsion is investigated using a displacement function φ. A governing differential equation for the stability of thin cylindrical shells under combined loading of axial compression, external pressure, and torsion is derived. A method for the solutions of this equation is also presented. The advantage in using the present equation over the customary three differential equations for displacements is that only one trial solution is needed in solving the buckling problems as shown in the paper. Four possible combinations of boundary conditions for a simply supported edge are treated. The case of a cylinder under axial compression is carried out in detail. For two types of simple supported boundary conditions, SS1 and SS2, the minimum critical axial buckling stress is found to be 43.5 percent of the well-known classical value Eh/R3(1−ν2) against the 50 percent of the classical value presently known.

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

On A Formulation of the Elastic Stability Equations of Circular Cylindrical Shells Under Variable Internal Pressure

1985 ◽  
Vol 9 (2) ◽  
pp. 64-69
Author(s):  
J.L. Urrutia-Galicia ◽  
A.N. Sherbourne
Keyword(s):  
Mathematical Model ◽  
Internal Pressure ◽  
Cylindrical Shells ◽  
Direct Analysis ◽  
Elastic Stability ◽  
Equilibrium Path ◽  
Circular Cylindrical Shells ◽  
The Stability ◽  
Variable Internal Pressure ◽  
The Mathematical Model

The mathematical model of the stability analysis of circular cylindrical shells under arbitrary internal pressure is presented. The paper consists of a direct analysis of the equilibrium modes in the neighbourhood of the unperturbed principal equilibrium path. The final stability condition results in a completely symmetric differential operator which is then compared with current theories found in the literature.

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