Closure to “Discussion of ‘Buckling and Postbuckling Behavior of Clamped Shallow Spherical Shells Under Axisymmetric Ring Loads’” (1972, ASME J. Appl. Mech., 39, p. 637)

1972 ◽  
Vol 39 (2) ◽  
pp. 637-637
Author(s):  
N. Akkas ◽  
N. R. Bauld
Keyword(s):  
Postbuckling Behavior ◽  
Spherical Shells

Spherical Shells Like Hexagons: Cylinders Prefer Diamonds—Part 1

1973 ◽  
Vol 40 (2) ◽  
pp. 575-581 ◽  
Author(s):  
C. G. Lange ◽  
A. C. Newell
Keyword(s):  
Initial Conditions ◽  
Multiple Scale ◽  
Equation System ◽  
Differential Equation System ◽  
Postbuckling Behavior ◽  
Spherical Shells ◽  
Initial Imperfections ◽  
Numerical Studies ◽  
Substantial Bias ◽  
Diamond Configuration

The purpose of this paper is to describe the initial postbuckling behavior of cylindrical shells under axial compression. Our thesis is that, out of a single infinity of possible buckling configurations which all correspond to diamond-shaped patterns, the square diamond pattern dominates. We do not claim that this pattern will be seen under all circumstances; we do claim, however, that if no substantial bias is present in either the initial imperfections or initial conditions, a natural selection mechanism exists which favors the square diamond configuration. In this paper we carry out the analytic work. A multiple scale technique is used to describe both the dynamic interaction and evolution of competing diamond patterns and the propagation of spatial inhomogeneities. Stability analysis on the resulting differential equation system lends support to our stated thesis. In addition, some initial numerical studies are presented which verify our conclusions. Part 2 will be devoted to more extensive numerical experiments.

Buckling and Postbuckling Behavior of Clamped Shallow Spherical Shells Under Axisymmetric Ring Loads

1971 ◽  
Vol 38 (4) ◽  
pp. 996-1002 ◽  
Author(s):  
N. Akkas ◽  
N. R. Bauld
Keyword(s):  
Numerical Study ◽  
Postbuckling Behavior ◽  
Spherical Shells ◽  
Concentrated Load ◽  
Fixed Ring ◽  
Buckling Behavior ◽  
Load Carrying ◽  
Post Buckling ◽  
Shell Parameter ◽  
Shell Geometry

This paper presents the results of a numerical study of the buckling and initial post-buckling behavior of clamped shallow spherical shells under axisymmetric ring loads. This behavior is studied for a cap with fixed geometry when the location of the ring load is allowed to vary from the equivalent of a concentrated load at the apex to a location near the midpoint of the shell base radius, and for a fixed ring load location when the shell geometry is allowed to vary. It is found in both studies that a significant range of the geometric shell parameter λ exists such that buckling is accompanied by a loss in load-carrying capacity.

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 Stability Analysis of Imperfect Spherical Shells

1970 ◽  
Vol 37 (3) ◽  
pp. 629-634 ◽  
Author(s):  
A. Kalnins ◽  
V. Biricikoglu
Keyword(s):  
Stability Analysis ◽  
General Theory ◽  
Spherical Shell ◽  
Nonlinear Theory ◽  
Geometric Parameters ◽  
Postbuckling Behavior ◽  
Spherical Shells ◽  
The Stability ◽  
Asymptotic Character

A procedure is given for the analysis of axisymmetrically imperfect spherical shells which is not limited by the magnitude of the imperfections. The geometric parameters of the imperfect shell are expressed in terms of those of the perfect shell and known imperfection distribution, and the imperfect shell is solved directly by means of a nonlinear theory. As an application of the proposed procedure, the critical pressures for an axisymmetrically imperfect complete spherical shell are calculated. The results are compared with those predicted by Koiter’s general theory of initial postbuckling behavior, and their asymptotic character is verified.

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