General Instability of a Ring-Stiffened, Circular Cylindrical Shell Under Hydrostatic Pressure

1957 ◽  
Vol 24 (2) ◽  
pp. 269-277
Author(s):  
S. R. Bodner
Keyword(s):  
Cylindrical Shell ◽  
Hydrostatic Pressure ◽  
Differential Equations ◽  
Energy Method ◽  
Circular Cylindrical Shell ◽  
Orthotropic Shell ◽  
Simple Expression ◽  
Isotropic Shell ◽  
Numerical Examples ◽  
The Stability

Abstract The general instability load of a ring-stiffened, circular cylindrical shell under hydrostatic pressure is determined by analyzing an equivalent orthotropic shell. A set of differential equations for the stability of an orthotropic shell is derived and solved for the case of a shell with simple end supports. The solution is presented in terms of parameters of the ring-stiffened, isotropic shell, and a relatively simple expression for the general instability load is obtained. Some numerical examples and graphs of results are presented. In addition, an energy-method solution to the problem is outlined, and the energy and displacement functions that could be used in carrying out a Rayleigh-Ritz approximation are indicated.

Study on Stability of Functionally Graded Cylindrical Shells Subjected to Hydrostatic Pressure

2014 ◽  
Vol 580-583 ◽  
pp. 2920-2923 ◽  
Author(s):  
Xiao Wan Liu ◽  
Bin Liang ◽  
Rong Li
Keyword(s):  
Cylindrical Shell ◽  
Hydrostatic Pressure ◽  
Critical Pressure ◽  
Shell Theory ◽  
Volume Fraction ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Fitting Method ◽  
Wave Propagation Method ◽  
The Stability

The stability of submerged functionally graded (FG) cylindrical shell under hydrostatic pressure is examined in this paper. Based on the Flügges shell theory, the coupled frequency of submerged FG cylindrical shell is obtained, using wave propagation method and Newton method. Then the critical pressure of FG cylindrical shells is given by applying linear fitting method. Results are compared to known solutions, where these solutions exist. The effects of constituent materials, volume fraction, boundary condition and dimensions on the critical pressures of submerged FG cylindrical shell are illustrated by examples.

Internal Resonance and Nonlinear Vibrations of Eccentric Rotating Composite Laminated Circular Cylindrical Shell

2019 ◽  
Author(s):  
Tao Liu ◽  
Wei Zhang ◽  
Yan Zheng ◽  
Yufei Zhang
Keyword(s):  
Cylindrical Shell ◽  
Differential Equations ◽  
Internal Resonance ◽  
Nonlinear Vibrations ◽  
Multiple Scales ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Nonlinear Partial Differential Equations ◽  
Shear Deformation Theory ◽  
Internal Resonances

Abstract This paper is focused on the internal resonances and nonlinear vibrations of an eccentric rotating composite laminated circular cylindrical shell subjected to the lateral excitation and the parametric excitation. Based on Love thin shear deformation theory, the nonlinear partial differential equations of motion for the eccentric rotating composite laminated circular cylindrical shell are established by Hamilton’s principle, which are derived into a set of coupled nonlinear ordinary differential equations by the Galerkin discretization. The excitation conditions of the internal resonance is found through the Campbell diagram, and the effects of eccentricity ratio and geometric papameters on the internal resonance of the eccentric rotating system are studied. Then, the method of multiple scales is employed to obtain the four-dimensional nonlinear averaged equations in the case of 1:2 internal resonance and principal parametric resonance-1/2 subharmonic resonance. Finally, we study the nonlinear vibrations of the eccentric rotating composite laminated circular cylindrical shell systems.

Precise Stability Analysis of Stepped Telescopic Booms and Practical Algorithm

2013 ◽  
Vol 395-396 ◽  
pp. 871-876
Author(s):  
Liang Du ◽  
Peng Lan ◽  
Nian Li Lu
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Characteristic Equation ◽  
Energy Method ◽  
Cross Sectional ◽  
Component Method ◽  
Practical Algorithm ◽  
The Stability ◽  
Precise Expression ◽  
Constant Section

To analyze the stability of stepped telescopic booms accurately, using vertical and horizontal bending theory, this paper established the deflection differential equations of stepped column model of arbitrary sectioned telescopic boom, the stability were analyzed, and obtained the precise expression of the buckling characteristic equation; Took certain seven-sectioned telescopic booms as example, by comparing the results with ANSYS, the accuracy of the equations deduced in this paper was verified. Presented the equivalent component method for the stability analysis of multi-stepped column, the equivalent cross-sectional moment of inertia was deduced by energy method, thus the stability of stepped column equivalent to that of constant section component. By comparing the results with exact value, the precision of equivalent component method was verified which was convenient for stability analysis of telescopic boom.

Bending of Cord Composite Laminate Cylindrical Shells

2003 ◽  
Vol 70 (3) ◽  
pp. 364-373 ◽  
Author(s):  
A. J. Paris ◽  
G. A. Costello
Keyword(s):  
Cylindrical Shell ◽  
Differential Equations ◽  
Closed Form ◽  
Composite Laminate ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Axisymmetric Loading ◽  
Shell Axis

A theory for the bending of cord composite laminate cylindrical shells is developed. The extension-twist coupling of the cords is taken into account. The general case of a circular cylindrical shell with cord plies at various angles to the shell axis is considered. The differential equations for the displacements are derived. These equations are solved analytically in closed form for a shell subjected to axisymmetric loading and no in-plane tractions. The results of the current study are compared with the commonly used Gough-Tangorra and Akasaka-Hirano solutions.

Determining Critical States of Equilibrium of Plates and Shells Under Initial Stress

1942 ◽  
Vol 9 (1) ◽  
pp. A27-A30
Author(s):  
H. Hencky
Keyword(s):  
Cylindrical Shell ◽  
Energy Method ◽  
Virtual Work ◽  
The Body ◽  
Principle Of Virtual Work ◽  
Practical Applications ◽  
Fundamental Knowledge ◽  
Plates And Shells ◽  
The Stability

Abstract The purpose of this paper is to show that Rayleigh’s energy method, used by Timoshenko for the determination of critical loads in plates and shells, is capable of an important generalization. The work involved is a direct continuation of the energy method of Timoshenko and is based on the principle of virtual work. According to this principle the variation of the work of the outer forces together with the variation of the kinetic energy is equal to the variation of the elastic energy stored up in the body. The author develops a series of formulas, by means of which the stability of a cylindrical shell under various conditions of stress may be determined. The practical applications of these formulas, requiring only a fundamental knowledge of the mathematics of engineering, are illustrated by suitable examples.

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