Axisymmetrical Creep Buckling of Clamped Shallow Spherical Shells

1965 ◽  
Vol 32 (2) ◽  
pp. 323-330 ◽  
Author(s):  
Nai Chien Huang
Keyword(s):  
Large Deformations ◽  
Correspondence Principle ◽  
Applied Pressure ◽  
Critical Time ◽  
External Pressure ◽  
Governing Equations ◽  
Spherical Shells ◽  
Relaxation Of Stresses ◽  
Viscoelastic Shells ◽  
Shell Geometry

For a viscoelastic clamped shallow spherical shell, the vertical deflection due to uniformly distributed external pressure is a function of time. When time reaches a critical value, the shell may snap through suddenly. This critical time depends on the magnitude of the applied pressure as well as the shell geometry. The governing equations for large deformations of viscoelastic shells can be derived by applying the correspondence principle to the equivalent equations in the elastic case. The critical times for various shells under different pressures are evaluated numerically. If the deflection volume of the shell is a constant throughout the deformation process, the external pressure decreases due to relaxation of stresses in the viscoelastic shell. This decreasing external pressure is also calculated in this paper.

scholarly journals Non-linear buckling analysis of functionally graded shallow spherical shells

2009 ◽  
Vol 31 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Dao Huy Bich
Keyword(s):  
External Pressure ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Governing Equations ◽  
Spherical Shells ◽  
Buckling Loads ◽  
Linear Buckling ◽  
Non Linear ◽  
Linear Buckling Analysis

In the present paper the non-linear buckling analysis of functionally graded spherical shells subjected to external pressure is investigated. The material properties are graded in the thickness direction according to the power-law distribution in terms of volume fractions of the constituents of the material. In the formulation of governing equations geometric non-linearity in all strain-displacement relations of the shell is considered. Using Bubnov-Galerkin's method to solve the problem an approximated analytical expression of non-linear buckling loads of functionally graded spherical shells is obtained, that allows easily to investigate stability behaviors of the shell.

scholarly journals Imperfection Sensitivity of Externally Pressurized Spherical Shells

1967 ◽  
Vol 34 (1) ◽  
pp. 49-55 ◽  
Author(s):  
J. W. Hutchinson
Keyword(s):  
General Theory ◽  
Shell Thickness ◽  
Middle Surface ◽  
External Pressure ◽  
Postbuckling Behavior ◽  
Imperfection Sensitivity ◽  
Spherical Shells ◽  
Small Deviations ◽  
Severe Effect ◽  
Shell Geometry

The initial postbuckling behavior of a shallow section of a spherical shell subject to external pressure is studied within the context of Koiter’s general theory of postbuckling behavior. Imperfections in the shell geometry are shown to have the same severe effect on the buckling strengths of spherical shells as has been demonstrated for axially compressed cylindrical shells. Large reductions in the buckling pressure result from small deviations, relative to the shell thickness, of the shell middle surface from the perfect configuration.

On the Nonlinear Analysis Methodologies for Thin Spherical Shells Under External Pressure with Different Finite-Element Codes

1989 ◽  
Vol 33 (04) ◽  
pp. 318-325
Author(s):  
Dario Boote ◽  
Donatella Mascia
Keyword(s):  
Finite Element ◽  
Numerical Procedure ◽  
External Pressure ◽  
Experimental Investigations ◽  
Nonlinear Analyses ◽  
Spherical Shells ◽  
Double Curvature ◽  
Load Carrying ◽  
Material Load ◽  
Structure Collapse

Submersible structures consist merely of simple and double curvature thin-walled shells. For this kind of structure, collapse occurs due to the combined nonlinear action of buckling and plasticity of material. Load-carrying capacity may then be assessed mainly by two approaches: experimental investigations and step-by-step numerical procedures. In nonlinear analyses, the results obtained are influenced by the magnitude of the load increment adopted. Solution procedures are then required in order to choose adequate parameters for material failure description as well as elastic nonlinearity. The aim of this paper is to carry out a suitable numerical procedure whose reliability does not depend on the finite-element code adopted.

scholarly journals Stability-Ranking of Crystalline Ice Polymorphs Using Density-Functional Theory

Crystals ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 40
Author(s):  
Pralok K. Samanta ◽  
Christian J. Burnham ◽  
Niall J. English
Keyword(s):  
Density Functional Theory ◽  
Structure Prediction ◽  
Density Functional ◽  
Applied Pressure ◽  
External Pressure ◽  
Crystal Structure Prediction ◽  
Functional Theory ◽  
Stability Ranking ◽  
High Level ◽  
Basin Hopping

In this work, we consider low-enthalpy polymorphs of ice, predicted previously using a modified basin-hopping algorithm for crystal-structure prediction with the TIP4P empirical potential at three pressures (0, 4 and 8 kbar). We compare and (re)-rank the reported ice polymorphs in order of energetic stability, using high-level quantum-chemical calculations, primarily in the guise of sophisticated Density-Functional Theory (DFT) approaches. In the absence of applied pressure, ice Ih is predicted to be energetically more stable than ice Ic, and TIP4P-predicted results and ranking compare well with the results obtained from DFT calculations. However, perhaps not unexpectedly, the deviation between TIP4P- and DFT-calculated results increases with applied external pressure.

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.

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