The singular perturbation method applied to the nonlinear stability problem of a shallow spherical shell (II)

1990 ◽  
Vol 11 (3) ◽  
pp. 285-291 ◽  
Author(s):  
Kang Sheng-liang
Keyword(s):  
Singular Perturbation ◽  
Spherical Shell ◽  
Perturbation Method ◽  
Nonlinear Stability ◽  
Stability Problem ◽  
Shallow Spherical Shell ◽  
Singular Perturbation Method

Nonlinear Stability Analysis of the Vaulted Roofs With Corrosion Defects of Oil Storage Tank

2009 ◽  
Author(s):  
Baosheng Dong ◽  
Xinwei Zhao ◽  
Hongda Chen ◽  
Jinheng Luo ◽  
Zhixin Chen ◽  
...  
Keyword(s):  
Spherical Shell ◽  
Nonlinear Stability ◽  
Storage Tank ◽  
Critical Pressure ◽  
External Pressure ◽  
Shallow Spherical Shell ◽  
Nonlinear Stability Analysis ◽  
Spherical Shells ◽  
Oil Storage ◽  
Oil Storage Tank

The vaulted roofs of oil storage tank are usually designed as the shallow spherical shells subjecting to a uniform external pressure, which have been widely observed that these shallow spherical shells undergo various levels of corrosion in their employing conditions. It is important to assess the stability of these local weaken shallow spherical roofs due to corrosion for preventing them from occurring unexpected buckling failure. In this paper, the uniform eroded part of a shallow spherical oil tank vaulted roof is simplified as a shallow spherical shell with elastic supports. Based on the simplification, a general pathway to calculate the critical pressure of eroded shallow spherical shell is proposed. The modified iteration method considering large deflection of the shell is applied to solve the problem of nonlinear stability of the shallow spherical shells, and then the second-order approximate analytical solution is obtained. The critical pressure calculated by this method is consistent with the classical numerical results and nonlinear finite element method, and the calculation errors are less than 10%. It shows that it is feasible to apply the method proposed here.

Singular Perturbation Method for Solving Non-Linear Vibration of Stay Cable (I) - Theory Research

2011 ◽  
Vol 147 ◽  
pp. 112-116
Author(s):  
Zhi Hong Ran ◽  
Jun Tong Qu ◽  
Fei He ◽  
Sheng Miao
Keyword(s):  
Singular Perturbation ◽  
Perturbation Method ◽  
Stay Cable ◽  
Linear Vibration ◽  
Singular Perturbation Method ◽  
Cable Structure ◽  
Non Linear ◽  
Cable Force ◽  
Set Up ◽  
Theory Research

In order to solve the difficult in calculating cable vibration, the non-linear dynamic model of cable was set up with geometrical non-linearity. The differential equation was solved using the singular perturbation method. The analytical expression of frequency and form function was deduced. The expression can be widely used for the field of measurement of cable force and identification of parameter in cable structure.

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