Application of the Point-Matching Method to Shallow-Spherical-Shell Theory

1962 ◽  
Vol 29 (4) ◽  
pp. 745-747 ◽  
Author(s):  
H. D. Conway ◽  
A. W. Leissa
Keyword(s):  
Spherical Shell ◽  
Shell Theory ◽  
Shallow Spherical Shell ◽  
Circular Pipe ◽  
Radial Load ◽  
Matching Method ◽  
Spherical Shells ◽  
Point Matching ◽  
Circular Base

Using Reissner’s [1] theory of the bending of shallow spherical shells, two unsymmetrical problems are investigated by the method of point-matching. The first is a uniformly loaded spherical shell clamped on a square base, numerical values of the moments and membrane forces being obtained and compared with the corresponding values for the case of a clamped circular base. The second problem is a spherical shell with a rigid elliptical insert, the latter carrying a central radial load. This gives information concerning the problem of a spherical shell which is pierced at an angle by a relatively rigid circular pipe.

Stresses in a Spherical Shell With a Circular Elastic Inclusion

1974 ◽  
Vol 96 (3) ◽  
pp. 228-233
Author(s):  
P. Prakash ◽  
K. P. Rao
Keyword(s):  
Differential Equations ◽  
Spherical Shell ◽  
Elastic Inclusion ◽  
Circular Inclusion ◽  
Shallow Spherical Shell ◽  
Spherical Shells ◽  
Hankel Functions ◽  
Circular Elastic Inclusion ◽  
Rigid Circular Inclusion

The problem of a circular elastic inclusion in a thin pressurized spherical shell is considered. Using Reissner’s differential equations governing the behavior of a thin shallow spherical shell, the solutions for the two regions are obtained in terms of Bessel and Hankel functions. Particular cases of a rigid circular inclusion free to move with the shell and a clamped rigid circular inclusion are also considered. Results are presented in nondimensional form which will greatly facilitate their use in the design of spherical shells containing a rigid or an elastic inclusion.

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.

Nonlinear Dynamic Response and Active Control of Piezoelastic Laminated Shallow Spherical Shells with Damage

2011 ◽  
Vol 21 (6) ◽  
pp. 783-809 ◽  
Author(s):  
Mao Yiqi ◽  
Fu Yiming ◽  
Tian Yanping
Keyword(s):  
Dynamic Response ◽  
Spherical Shell ◽  
Vibration Control ◽  
Analytical Model ◽  
Constitutive Relations ◽  
Collocation Point ◽  
Shallow Spherical Shell ◽  
Geometrical Parameters ◽  
Orthogonal Collocation ◽  
Spherical Shells

Based on Talreja’s damage model with tensor valued internal state variables and geometric nonlinear theory, the constitutive relations for a moderately thick shallow spherical shell with damage are derived. The distribution of electric potential along the thickness direction in the piezoelectric layer is simulated by a sinusoidal function, and accordingly the dynamic analytical model for the cross-ply laminated moderately thick piezoelectric shallow spherical shell is established. Using the negative velocity feedback control algorithm, an analytical model for active vibration control of the piezoelectric laminated moderately thick piezoelectric shallow spherical shell is built when the damage effect is considered. And the solutions to the whole problem are obtained with synthetical utilization of the orthogonal collocation point method and the Newark method. In numerical examples, the effects of damage, piezoelectric effect, and the structure’s geometrical parameters on the dynamic response and vibration control of the piezoelastic laminated shallow spherical shells with damage are investigated.

On the Initial Response of a Spherical Shell to a Concentrated Force

1962 ◽  
Vol 29 (4) ◽  
pp. 689-695 ◽  
Author(s):  
M. A. Medick
Keyword(s):  
Spherical Shell ◽  
Shallow Shell ◽  
Shell Theory ◽  
Initial Response ◽  
Shallow Spherical Shell ◽  
Restricted Class ◽  
Concentrated Force ◽  
Elastic Shells

This paper is concerned with the initial response of a restricted class of thin elastic shells to localized transient loadings. Attention is restricted to those shells which are essentially spherical and shallow in a neighborhood of the loading. The initial response within this neighborhood can be approximated by the response of a (shallow) spherical shell segment to a concentrated force within the framework of a modified shallow-shell theory.

Stresses in Spherical Shells Due to Local Loadings

1973 ◽  
Vol 17 (01) ◽  
pp. 19-22
Author(s):  
Robert Kao ◽  
Nicholas Perrone
Keyword(s):  
Spherical Shell ◽  
Shallow Shell ◽  
Shell Theory ◽  
Maximum Stress ◽  
Large Deflection ◽  
Local Loading ◽  
Spherical Shells ◽  
Finite Difference Approximations ◽  
Practical Design ◽  
Maximum Stresses

The maximum stresses are obtained for a spherical shell that is lifted or towed by a cable or any mechanical power hoist. In view of the highly localized nature of the maximum stress induced in a spherical shell due to local loading, the nonlinear (large deflection) shallow-shell theory is adopted for the analysis. A nonlinear relaxation technique in conjunction with finite difference approximations is introduced for the numerical integration. Results obtained here are presented in the graphic form that may be readily used by engineers in practical design.

Analysis of Electromagnetic Scattering from a Conducting Spherical Shell by the 3D Point Matching Method with Mode Expansion

2014 ◽  
Vol E97.C (7) ◽  
pp. 714-717
Author(s):  
Shinichiro OHNUKI ◽  
Kenichiro KOBAYASHI ◽  
Seiya KISHIMOTO ◽  
Tsuneki YAMASAKI
Keyword(s):  
Spherical Shell ◽  
Electromagnetic Scattering ◽  
Matching Method ◽  
Point Matching ◽  
Mode Expansion

A Comparison of Theoretical and Experimental Results From Spherical Shells With a Single Radially Attached Nozzle

1967 ◽  
Vol 89 (3) ◽  
pp. 333-338 ◽  
Author(s):  
F. J. Witt ◽  
R. C. Gwaltney ◽  
R. L. Maxwell ◽  
R. W. Holland
Keyword(s):  
Spherical Shell ◽  
Internal Pressure ◽  
Experimental Results ◽  
Strain Gages ◽  
Spherical Shells ◽  
Axial Thrust ◽  
Outside Diameter ◽  
Theoretical Results

A series of steel models having single nozzles radially and nonradially attached to a spherical shell is presently being examined by means of strain gages. Parameters being studied are nozzle dimensions, length of internal nozzle protrusions, and angles of attachment. The loads are internal pressure and axial thrust and moment loadings on the nozzle. This paper presents both experimental and theoretical results from six of the configurations having radially attached nozzles for which the sphere dimensions are equal and the outside diameter of the attached nozzle is constant. In some instances the nozzle protrudes through the vessel.

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