Abstract
The behavior of an annular plate, free at its inner edge and simply supported at the outer one, is investigated experimentally. The loading is a compressive implane force which is uniformly applied at the outer boundary. Deformations and strains are explored over sub, trans and postbuckling regions. Experimental results for the buckling loads, obtained by different methods, are compared. Comparison is also made with existing theoretical data. Fair to good agreement is found between theory and experiments, especially with respect to circumferential strains. The important influence that initial geometrical imperfections can have on the behavior of the compressed plate is also discussed.
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Abbreviations
- A, B :
-
constants given by eq (3)
- a, b :
-
radii of outer and inner edges, respectively (mm)
- c :
-
constant in eq (7) (mm)
- D :
-
flexural rigidity of the plate =Eh 3/12 (1−v 2) (N−mm)
- E :
-
modulus of elasticity (MPa)
- h :
-
plate thickness (mm)
- \(\bar p\) :
-
oil pressure in the rubber tube (MPa)
- \(\bar p_o \) :
-
pressure losses (MPa)
- P :
-
compressive force per unit length (N/mm)
- P cr :
-
critical compressive force per unit length (N/mm)
- r :
-
distance from center (mm)
- w :
-
transverse deflection (mm)
- z :
-
dimensionless load parameter = Pa2/D
- z 1 :
-
dimensionless critical load parameter =P cr a2/D
- ∇2 :
-
Laplacian (d 2/dr 2+1/r d/dr)
- μ:
-
ratio between the radiib anda
- ν:
-
Poisson's ratio
- σ r ,Ãθ :
-
radial and circumferential stresses, respectively (MPa)
- θ:
-
circumferential angle (deg)
- ∈ r ,∈θ :
-
average radial and circumferential strains, respectively (μm/m)
References
Meissner, E., “Uber das Knicken Kriesringförmiger Scheiben,”Shweiserische Bauzeitung,101,87–89 (1933).
Timoshenko, S. P. and Gere, J. M., Theory of Elastic Stability, McGraw Hill Book Co., Inc., 2nd Ed. (1961).
Timoshenko, S. P. andGoodier, J. M., Theory of Elasticity, McGraw-Hill-Kogakusha, Tokyo, 389–392 (1970).
Feder, M., “Axisymmetric Buckling of an Annular Plate,” Astronautical Research, 535–546, Ed. by L. G. Napolitano, D. Reidel Publishing Co. (1971).
Donnell, L. H., On the Application of Southwell's Method for the Analysis of Buckling Tests, Stephen Timoshenko 60th Anniversary Volume, 27–38, McGraw-Hill Book Co. (1938).
Horton, W. H., Cundari, F. L. andJohnson, R. W., “The Analysis of Experimental Data Obtained from Stability Studies on Elastic Column and Plate Structures,”Israel J. of Tech.,5 (1–2),104–113 (1967).
Roorda, J., “Some Thoughts on the Southwell Plot,”J. of the Engrg. Mech. Div., Proc. of the ASCE,96 (EM6),37–48 (1967).
Timoshenko, S. and Winowsky-Krieger, S., Theory of Plates and Shells, McGraw-Hill-Kogakusha Co., 2nd Ed. (1959).
Hoff, N. J., Bruno, A. B. andCoan, J. M., “The Development of a Technique for Testing Stiff Panels in Edge Compression,”Proc. of the SESA,V (II),14–24 (1948).
Majundar, S., “Buckling of a Thin Annular Plate Under Uniform Compression,”AIAA J.,9 (9),1701–1707, (1971).
Rosen, A. andLibai, A., “Stability Behavior and Vibrations of an Annular Plate Under Uniform Compression,”TAE Report 229, Technion-Israel Institute of Technology, Dept. of Aero. Engineering, Haifa, Israel (October 1974).
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Rosen, A., Libai, A. Stability and behavior of an annular plate under uniform compression. Experimental Mechanics 16, 461–467 (1976). https://doi.org/10.1007/BF02324103
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DOI: https://doi.org/10.1007/BF02324103