Bending Solutions of Sectorial Mindlin Plates from Kirchhoff Plates
Publication: Journal of Engineering Mechanics
Volume 126, Issue 4
Abstract
This study presents exact relationships between the bending solutions of sectorial plates based on the Kirchhoff (or classical thin) plate theory and the Mindlin plate theory. While the former plate theory neglects the effect of transverse shear deformation, the latter theory allows for this effect, which becomes significant when dealing with thick plates and sandwich plates. The considered sectorial plates have simply supported radial edges, while the circular curved edge may be either simply supported, or clamped or free. The availability of such relationships allow easy conversion of the existing Kirchhoff sectorial plate solutions into the corresponding Mindlin solutions, thus bypassing the need to solve the more complicated bending equations of the Mindlin plates. The use of the relationships is illustrated using some sectorial plate examples, and sample solutions obtained were checked with previous researchers' results and those computed from the software ABAQUS.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
ABAQUS/standard user's manual (version 5.8). (1998). Vols. 1–3, Hibbitt, Karlsson & Sorensen, Inc., Pawtucket, R.I.
2.
Cheung, M. S., and Chan, M. Y. T. (1981). “Static and dynamic analysis of thin and thick sectorial plates by the finite strip method.” Comp. and Struct., 14(1–2), 79–88.
3.
Deverall, L. I., and Thorne, C. J. (1951). Bending of thin ring-sector plates.” Trans. ASME, J. Appl. Mech., 18, 359–363.
4.
Kreyszig, E. (1993). Advanced engineering mathematics, 7th Ed., Wiley, New York.
5.
Mansfield, E. H. (1989). The bending and stretching of plates, 2nd Ed., Cambridge University Press, Cambridge, U.K.
6.
Mindlin, R. D. (1951). “Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates.” Trans. ASME, J. of Appl. Mech., 18, 1031–1036.
7.
Reismann, H. (1988). Elastic plates: Theory and application. Wiley, New York.
8.
Timoshenko, S. P., and Woinowsky-Krieger, S. (1959). Theory of plates and shells. McGraw-Hill, New York.
9.
Wang, C. M. (1997). “Relationships between Mindlin and Kirchhoff bending solutions for tapered circular and annular plates.” Engrg. Struct., 19(3), 255–258.
10.
Wang, C. M., and Alwis, W. A. M. (1995). “Simply supported Mindlin plate deflections using Kirchhoff plates.”J. Engrg. Mech., ASCE, 121(12), 1383–1385.
11.
Wang, C. M., and Lee, K. H. (1996). “Deflection and stress-resultants of axisymmetric Mindlin plates in terms of Kirchhoff solutions.” Int. J. Mech. Sci., 38(11), 1179–1185.
12.
Wang, C. M., Lim, G. T., and Lee, K. H. (1999). “Relationships between Kirchhoff and Mindlin bending solutions for Levy plates.” J. Appl. Mech., 66(2), 541–545.
Information & Authors
Information
Published In
History
Received: Jan 26, 1999
Published online: Apr 1, 2000
Published in print: Apr 2000
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.