Experimental Buckling Modes of Clamped Shallow Shells Under Concentrated Load

1966 ◽  
Vol 33 (2) ◽  
pp. 297-304 ◽  
Author(s):  
F. A. Penning
Keyword(s):  
Elastic Stability ◽  
Plastic Behavior ◽  
Spherical Shells ◽  
Finite Area ◽  
Concentrated Load ◽  
Buckling Loads ◽  
Buckling Modes ◽  
Shallow Shells

Elastic stability of clamped shallow spherical shells subjected to a small finite-area load at the apex is studied experimentally. Upper and lower critical buckling loads and prebuckled and postbuckled deflections are found for λ between 10 and 17. Buckling modes have been observed and defined. Nonaxisymmetric deformations are noted. Shells for λ less than 8 1/2 exhibit plastic behavior and do not buckle.

On the Vibration and Stability of Finitely Deformed Shallow Spherical Shells

1965 ◽  
Vol 32 (1) ◽  
pp. 116-120 ◽  
Author(s):  
R. R. Archer ◽  
J. Famili
Keyword(s):  
Finite Difference ◽  
Spherical Shell ◽  
Frequency Spectrum ◽  
Excellent Agreement ◽  
Load Parameter ◽  
Spherical Shells ◽  
Buckling Loads ◽  
Buckling Modes ◽  
Difference Analysis ◽  
Finite Difference Analysis

Equations describing the asymmetric vibrations of a shallow spherical shell which has suffered a finite axisymmetric displacement due to axisymmetric loading are studied by means of a finite-difference analysis. Results are obtained which show a continuous variation of the frequency spectrum as a function of the load parameter ranging from the previously computed frequencies and modes of the unloaded shell to the modes corresponding to vanishing frequencies which reveal the asymmetric buckling modes and loads for the shell. Excellent agreement with earlier work is found for both limiting cases thus providing an independent check on the asymmetric buckling loads recently computed by Huang.

Propagation of Axisymmetric Waves in an Unlimited Elastic Shell

1960 ◽  
Vol 27 (4) ◽  
pp. 690-695 ◽  
Author(s):  
A. Kalnins ◽  
P. M. Naghdi
Keyword(s):  
Spherical Shell ◽  
Entire Range ◽  
Energy Input ◽  
Elastic Shell ◽  
Mechanical Impedance ◽  
Stress Waves ◽  
Axisymmetric Stress ◽  
Spherical Shells ◽  
Concentrated Load ◽  
Shallow Shells

This investigation is concerned with the propagation of axisymmetric stress waves in unlimited thin shallow elastic spherical shells. In particular, a solution is obtained for an unlimited shallow spherical shell subjected to a harmonically oscillating concentrated load at the apex. This solution, exact within the scope of the linear theory of shallow shells, has an outward propagating wave character in the entire range of forcing frequency. Appropriate expressions for the mechanical impedance and the energy input are derived, and numerical results are obtained for the axial displacement corresponding to various forcing frequencies.

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.

The Role of Adhesive in the Load Response of Adhesively Bonded Aluminum Hat Sections Under Axial Compression

2001 ◽  
Author(s):  
Jianping Lu ◽  
Golam M. Newaz ◽  
Ronald F. Gibson
Keyword(s):  
Compressive Strength ◽  
Plastic Collapse ◽  
Adhesively Bonded ◽  
Buckling Mode ◽  
Buckling Loads ◽  
Buckling Modes ◽  
Load Response ◽  
Peak Loads ◽  
Post Buckling

Abstract Aluminum hat section, either adhesively bonded or unbonded, experiences buckling, post buckling and plastic collapse when axially compressed. However, there exist obvious differences in the load response between the bonded and unbonded hat sections. Finite element eigenvalue buckling analysis is carried out to predict the buckling load and mode. Experiments show that when adhesively bonded hat sections begin to buckle there is a transformation from the first buckling mode to the higher ones, while the unbonded hat sections develop the post buckling based on the lowest buckling mode. The different buckling modes result in not only different buckling loads but different peak loads of the hat sections as well. Finally, the ultimate compressive strength formulae are proposed for the hat sections.

Optimal Forms of Shallow Shells With Circular Boundary, Part 2: Maximum Buckling Load

1984 ◽  
Vol 51 (3) ◽  
pp. 531-535 ◽  
Author(s):  
R. H. Plaut ◽  
L. W. Johnson
Keyword(s):  
Critical Load ◽  
Elastic Shell ◽  
Material Surface ◽  
Fundamental Vibration ◽  
Uniform Loading ◽  
Concentrated Load ◽  
Shallow Shells ◽  
Simply Supported ◽  
Circular Boundary ◽  
Boundary Part

In Part 1, optimal forms were determined for maximizing the fundamental vibration frequency of a thin, shallow, axisymmetric, elastic shell with given circular boundary. Our objective in this part is to maximize the critical load for buckling under a uniformly distributed load or a concentrated load at the center. Again, the shell form is varied and the material, surface area, and uniform thickness of the shell are specified. Both clamped and simply supported boundary conditions are considered for the case of uniform loading, while one example is presented involving a concentrated load acting on a clamped shell. The optimality condition leads to forms that have zero slope at the boundary if it is clamped. The maximum critical load is sometimes associated with a limit point and sometimes with a bifurcation point. It is often substantially higher than the critical load for the corresponding spherical shell.

Erratum: "Elastic Stability of Near-Perfect Shallow Spherical Shells"

AIAA Journal ◽  
1964 ◽  
Vol 2 (4) ◽  
pp. 0784b-0784b
Author(s):  
M. A. KRENZKE ◽  
T. J. KIERNAN
Keyword(s):  
Elastic Stability ◽  
Spherical Shells

Small-Scale Yielding at the Tip of a Through-Crack in a Shell

1980 ◽  
Vol 102 (2) ◽  
pp. 167-173 ◽  
Author(s):  
J. D. Achenbach ◽  
T. Bubenik
Keyword(s):  
Nonlinear Behavior ◽  
Crack Edge ◽  
Small Scale ◽  
Small Scale Yielding ◽  
Spherical Shells ◽  
Shallow Shells ◽  
Scale Yielding ◽  
Hardening Curve ◽  
Thickness Variations ◽  
Independent Integral

Deformation theory is used to model plastic deformation at the tip of a through-crack in a thin shell. In the vicinity of the crack the shell is subjected to both stretching and bending, but stretching is assumed to dominate. Thus the stresses are tensile, but with a nonuniform distribution through the thickness, which depends on the material properties as well as on the geometry. The nonlinear near-tip fields (which are singular) have been analyzed asymptotically. Cracks in shallow shells and spherical shells have been investigated in some detail. It is shown that the angular variations are the same as for generalized plane-stress plate problems. Assuming small-scale yielding a path-independent integral, which is valid in a region close to the crack edge, is used to connect the nonlinear near-tip fields with the corresponding singular parts of the linear fields. It is shown that the nonlinear behavior significantly affects the through-the-thickness variations of the near-tip fields. The singular parts of the membrane stresses tend to become more uniform through the thickness of the shell with a flatter strain-hardening curve.

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