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.

Certain Solution of Contact Problem for Spherical Shell

2013 ◽  
Vol 542 ◽  
pp. 179-191 ◽  
Author(s):  
Henryk Sanecki ◽  
Łukasz Wachowicz
Keyword(s):  
Contact Problem ◽  
Spherical Shell ◽  
Load Distribution ◽  
Thin Shell ◽  
Shell Theory ◽  
Complex Form ◽  
Finite Area ◽  
Concentrated Force ◽  
Thin Shell Theory ◽  
Small Deformations

A formulation of a contact problem for a spherical shell is presented in the paper. It uses a certain analytical-numerical solution for the analysis of an elastic complete sphere subjected to a concentrated force and associated body forces. Assumptions and equations of thin shell theory of small deformations and displacements are applied to the problem. Good numerical efficiency is achieved due to a solving functionZintroduced in a complex form while the concentrated force was distributed over a small finite area. Some examples are presented to illustrate the solution and an influence of the size of assumed area of load distribution. An application of the solution to the formulation of the contact problem of the spherical shell resting on several separate supports is presented.

scholarly journals Static bistability of spherical caps

2018 ◽  
Vol 474 (2213) ◽  
pp. 20170910 ◽  
Author(s):  
Matteo Taffetani ◽  
Xin Jiang ◽  
Douglas P. Holmes ◽  
Dominic Vella
Keyword(s):  
Finite Element ◽  
Spherical Shell ◽  
Shallow Shell ◽  
Shell Theory ◽  
Solid Angle ◽  
The Other ◽  
Stable States ◽  
Good Account ◽  
Spherical Caps ◽  
Inside Out

Depending on its geometry, a spherical shell may exist in one of two stable states without the application of any external force: there are two ‘self-equilibrated’ states, one natural and the other inside out (or ‘everted’). Though this is familiar from everyday life—an umbrella is remarkably stable, yet a contact lens can be easily turned inside out—the precise shell geometries for which bistability is possible are not known. Here, we use experiments and finite-element simulations to determine the threshold between bistability and monostability for shells of different solid angle. We compare these results with the prediction from shallow shell theory, showing that, when appropriately modified, this offers a very good account of bistability even for relatively deep shells. We then investigate the robustness of this bistability against pointwise indentation. We find that indentation provides a continuous route for transition between the two states for shells whose geometry makes them close to the threshold. However, for thinner shells, indentation leads to asymmetrical buckling before snap-through, while also making these shells more ‘robust’ to snap-through. Our work sheds new light on the robustness of the ‘mirror buckling’ symmetry of spherical shell caps.

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 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.

Zero Gravity Validation of Smart Aperture Antennas

1999 ◽  
Author(s):  
Hwan-Sik Yoon ◽  
Gregory Washington
Keyword(s):  
Spherical Shell ◽  
Analytical Model ◽  
Stress Function ◽  
Spherical Shape ◽  
Element Model ◽  
Shallow Spherical Shell ◽  
Zero Gravity ◽  
Governing Equations ◽  
Homogeneous Solutions ◽  
Calculated Stress

Abstract In this study, a smart aperture antenna of spherical shape is modeled and experimentally verified. The antenna is modeled as a shallow spherical shell with a small hole at the apex for mounting. Starting from five governing equations of the shallow spherical shell, two governing equations are derived in terms of a stress function and the axial deflection using Reissner’s approach. As actuators, four PZT strip actuators are attached along the meridians separated by 90 degrees respectively. The forces developed by the actuators are considered as distributed pressure loads on the shell surface instead of being applied as boundary conditions like previous studies. This new way of applying the actuation force necessitates solving for the particular solutions in addition to the homogeneous solutions for the governing equations. The amount of deflections is evaluated from the calculated stress function and the axial deflection. In addition to the analytical model, a finite element model is developed to verify the analytical model on the various surface positions of the reflector. Finally, an actual working model of the reflector is built and tested in a zero gravity environment, and the results of the theoretical model are verified by comparing them to the experimental data.

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