Finite Deflections of Thin Shallow Spherical Shells Under Axisymmetrical Line Load and Uniform Pressure

1967 ◽  
Vol 34 (4) ◽  
pp. 1022-1024 ◽  
Author(s):  
Chuen-Yuan Chia
Keyword(s):  
Uniform Pressure ◽  
Finite Deflections ◽  
Spherical Shells ◽  
Line Load

Dynamic Vibrations and Stresses in Elastic Cylinders and Spheres

1966 ◽  
Vol 33 (4) ◽  
pp. 825-830 ◽  
Author(s):  
G. Cinelli
Keyword(s):  
Circular Cylindrical Shell ◽  
Hankel Transform ◽  
Dynamic Loads ◽  
Torsional Motion ◽  
Spherical Shells ◽  
Symmetric Motion ◽  
Line Load ◽  
Elastic Cylinders ◽  
Finite Hankel Transform ◽  
Cylinders And Spheres

A new finite Hankel transform [1] is used to find the transient displacement and stresses in thick elastic cylinders and spheres when the surfaces are subjected to dynamic loads for the following problems: (a) Pure radial and torsional motion of an infinitely long circular cylindrical shell; (b) radially symmetric motion of a spherical shell. The loads applied to both surfaces of the cylindrical and spherical shells are completely arbitrary functions of space (for the torsional case) and time. Employing the solutions obtained for the arbitrary loads, the spatial and temporal positions of these loads are then specialized to standard forms, such as a line load, band load, impulse, and so on, and the corresponding motion and stresses are found.

Large Deflection of Axisymmetrically Loaded Spherical Caps

1976 ◽  
Vol 27 (1) ◽  
pp. 29-39
Author(s):  
Chuen-Yuan Chia
Keyword(s):  
Axisymmetric Deformation ◽  
Uniform Pressure ◽  
Spherical Cap ◽  
Line Load ◽  
Simply Supported ◽  
Pressure Line ◽  
Edge Conditions ◽  
Method Of Solution ◽  
Linear Behaviour ◽  
Spherical Caps

SummaryThis study is an investigation of the non-linear behaviour of an elastic spherical cap under the assumption of axisymmetric deformation. The types of axisymmetric loading under consideration are partially loaded uniform pressure, line load, “cosine” load with the maximum intensity at the apex and the combined action of uniform pressure and line load. The edge of the cap is assumed to be rigidly clamped, hinged, and unrestrainedly simply-supported. The method of solution is an extension of the iterative procedure for the integral equations formulated by Budiansky for uniformly loaded, clamped caps. In the cases of hinged and unrestrainedly simply-supported edges, the critical loads for the axisymmetric snap-buckling are presented for different types of loading and various values of the geometrical cap parameter. In the case of a clamped edge the load-deflection curves are established until no solution can be found for further increasing the load. The load corresponding to the limit point on the load-deflection curve is the critical load if the axisymmetric snap-buckling exists. The graphical results are presented for load-deflection curves, deflection profiles, bending moments, transverse shear and interaction of buckling pressures and buckling line loads. The present results are in good agreement with available data for uniform pressure distributed over the entire surface of the cap with three sets of edge conditions and over the central portion of a clamped cap.

Nonlinear Buckling Interaction for Spherical Shells Subject to Pressure and Probing Forces

2017 ◽  
Vol 84 (6) ◽  
Author(s):  
John W. Hutchinson ◽  
J. Michael T. Thompson
Keyword(s):  
Internal Pressure ◽  
Energy Barrier ◽  
Constant Pressure ◽  
External Pressure ◽  
Constant Volume ◽  
Uniform Pressure ◽  
Loading Conditions ◽  
Spherical Shells ◽  
Nonlinear Buckling ◽  
Axisymmetric State

Elastic spherical shells loaded under uniform pressure are subject to equal and opposite compressive probing forces at their poles to trigger and explore buckling. When the shells support external pressure, buckling is usually axisymmetric; the maximum probing force and the energy barrier the probe must overcome are determined. Applications of the probing forces under two different loading conditions, constant pressure or constant volume, are qualitatively different from one another and fully characterized. The effects of probe forces on both perfect shells and shells with axisymmetric dimple imperfections are studied. When the shells are subject to internal pressure, buckling occurs as a nonaxisymmetric bifurcation from the axisymmetric state in the shape of a mode with multiple circumferential waves concentrated in the vicinity of the probe. Exciting new experiments by others are briefly described.

Marangoni Convection in Spherical Shells

2005 ◽  
Author(s):  
Pravin Subramanian ◽  
Abdelfattah Zebib
Keyword(s):  
Marangoni Convection ◽  
Spherical Shells
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