Axisymmetric Buckling of Reddy Circular Plates on Pasternak Foundation
Publication: Journal of Engineering Mechanics
Volume 127, Issue 3
Abstract
Presented herein are the exact axisymmetric buckling solutions of Reddy circular plates on the Pasternak foundation and subjected to a uniform radial load. The boundary conditions of the circular plates covered in this study are (1) simply supported edges; (2) clamped edges; and (3) simply supported edges with elastic rotational restraints. The Reddy buckling solutions are expressed in terms of the corresponding well-known Kirchhoff buckling solutions of circular plates without the elastic foundation. Sample buckling results of Reddy plates are also presented, which should be useful as benchmark solutions for testing numerical solutions and techniques.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Dumir, P. C. ( 1988). “Large deflection axisymmetric analysis of orthotropic annular plates on elastic foundations.” Int. J. Solids and Struct., 24, 777–787.
2.
Irschik, H. ( 1985). “Membrane-type eigenmotions of Mindlin plates.” Acta Mechanica, 55, 1–20.
3.
Kerr, A. D. ( 1962). “On the instability of circular plates.” J. Aero. Sci. (Readers' Forum), 29(4), 486–487.
4.
Mindlin, R. D. ( 1951). “Influence of rotary inertia and shear in flexural motion of isotropic, elastic plates.” J. Appl. Mech., 18, 1031–1036.
5.
Nosier, A., and Reddy, J. N. ( 1992). “On boundary layer and interior equations for higher-order theories of plates.” Z. Angew. Math. Mech., 72, 657–666.
6.
Pasternak, P. L. ( 1954). “On a new method of analysis of an elastic foundation by means of two foundation constants.” Gos. Izd. Lit. po Strait I Arkh, Moscow.
7.
Reddy, J. N. ( 1984). “A simple higher-order theory for laminated composite plates.” J. Appl. Mech., 51, 745–752.
8.
Reddy, J. N. ( 1997). Mechanics of laminated composite plates: Theory and analysis, CRC, Boca Raton, Fla.
9.
Reismann, H. ( 1952). “Bending and buckling of an elastically restrained circular plate.” J. Appl. Mech., 167–172.
10.
Smaill, J. S. ( 1991). “Large deflection response of annular plates on Pasternak founations.” Int. J. Solids and Struct., 27(8), 1073–1084.
11.
Spiegel, M. R. ( 1999). Mathematical handbook of formulas and tables, Int. Ed., Schaum's Outline Ser., McGraw-Hill, Singapore.
12.
Wang, C. M. ( 1994). “Natural frequencies formula for simply supported Mindlin plates.” J. Vibration and Acoustics, 116(4), 536–540.
13.
Wang, C. M. ( 1995a). “Buckling of polygonal and circular sandwich plates.” AIAA J., 33(5), 962–964.
14.
Wang, C. M. ( 1995b). “Allowance for prebuckling deformations in buckling load relationship between Mindlin and Kirchhoff simply supported plates of general polygonal shape.” Engrg. Struct., 17(6), 413–418.
15.
Wang, C. M. ( 1996). “Vibration frequencies of simply supported polygonal sandwich plates via Kirchhoff solutions.” Sound and Vibration, 190(2), 255–260.
16.
Wang, C. M. ( 1997). “Relationships between Mindlin and Kirchhoff bending solutions for tapered circular and annular plates.” Engrg. Struct., 19(3), 255–258.
17.
Wang, C. M., and Alwis, W. A. M. (1995). “Simply supported polygonal Mindlin plate deflections using Kirchhoff plates.”J. Engrg. Mech., ASCE, 121(12), 1383–1385.
18.
Wang, C. M., and Lee, K. H. ( 1996). “Deflection and stress-resultants of axisymmetric Mindlin plates in terms of corresponding Kirchhoff solutions.” Int. J. Mech. Sci., 38(11), 1179–1185.
19.
Wang, C. M., and Reddy, J. N. ( 1997). “Buckling load relationship between Reddy and Kirchhoff plates of polygonal shape with simply supported edges.” Mech. Res. Comm., 24(1), 103–108.
20.
Wang, C. M., Reddy, J. N., and Lee, K. H. ( 2000). Shear deformable beams and plates: Relationships with classical solutions, Elsevier, Oxford, England.
21.
Wang, Q. S., He, B. C., and Wang, D. J. ( 1992). “Dynamic quantitative characteristics of discrete model of second order continuous system.” Vibration and Shock, 3, 7–12.
22.
Wang, Q. S., and Wang, D. J. ( 1991). “General proof for qualitative characteristics of continuous and discrete beam system.” Acta Mechanica Sinica, 1, 99–102.
Information & Authors
Information
Published In
History
Received: Apr 11, 2000
Published online: Mar 1, 2001
Published in print: Mar 2001
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.