The method of multiple scales applied to the nonlinear stability problem of a truncated shallow spherical shell of variable thickness with the large geometrical parameter

2001 ◽  
Vol 22 (10) ◽  
pp. 1198-1209
Author(s):  
Kang Sheng-liang
Keyword(s):  
Spherical Shell ◽  
Nonlinear Stability ◽  
Variable Thickness ◽  
Geometrical Parameter ◽  
Stability Problem ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Shallow Spherical Shell

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.

The equivalence between two perturbation methods in weakly nonlinear stability theory for parallel shear flows

1989 ◽  
Vol 424 (1867) ◽  
pp. 373-392 ◽  
Keyword(s):  
Numerical Calculation ◽  
Nonlinear Stability ◽  
Stability Theory ◽  
Perturbation Methods ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Expansion Method ◽  
Normalization Condition ◽  
Weakly Nonlinear ◽  
Parallel Shear Flows

Two perturbation methods used in weakly nonlinear stability theory, namely, the method of multiple scales and the amplitude expansion method, are examined for their equivalence through formal analyses and numerical calculation of the Landau constants. The method of multiple scales is shown to give results equivalent to those obtained from the amplitude expansion formulation for slightly supercritical states if a normalization condition is applied to the fundamental mode. The convergence of the expansion in the method of multiple scales is also discussed.

Nonlinear stability of thin elastic circular shallow spherical shell under the action of uniform edge moment

1980 ◽  
Vol 1 (1) ◽  
pp. 71-90 ◽  
Author(s):  
Yeh Kai-yuan ◽  
Liu Zen-huai ◽  
Chang Chuan-dzi ◽  
Shue Ih-fan
Keyword(s):  
Spherical Shell ◽  
Nonlinear Stability ◽  
Shallow Spherical Shell

Nonlinear stability of double-deck reticulated circular shallow spherical shell

2010 ◽  
Vol 31 (3) ◽  
pp. 279-290 ◽  
Author(s):  
Jia-chu Xu ◽  
Yong Li ◽  
Fan Wang ◽  
Ren-huai Liu
Keyword(s):  
Spherical Shell ◽  
Nonlinear Stability ◽  
Shallow Spherical Shell

Inverse problem of the nonlinear stability of a spherical shell of variable thickness

1977 ◽  
Vol 13 (2) ◽  
pp. 112-116
Author(s):  
V. V. Gaidaichuk ◽  
E. A. Gotsulyak ◽  
V. I. Gulyaev
Keyword(s):  
Inverse Problem ◽  
Spherical Shell ◽  
Nonlinear Stability ◽  
Variable Thickness
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