Technical Briefs

A Generalized Reissner Theory for Large Axisymmetric Deflections of Circular Plates

[+] Author and Article Information
Raymond H. Plaut

Fellow ASME
Department of Civil and Environmental Engineering,
Virginia Polytechnic Institute and State University,
Blacksburg, VA 24061
e-mail: rplaut@vt.edu

Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received January 25, 2013; final manuscript received April 13, 2013; accepted manuscript posted September 3, 2013; published online September 18, 2013 Assoc. Editor: George Kardomateas.

J. Appl. Mech 81(3), 034502 (Sep 18, 2013) (3 pages) Paper No: JAM-13-1049; doi: 10.1115/1.4024413 History: Received January 25, 2013; Revised April 13, 2013; Accepted September 03, 2013

A generalized Reissner theory for axisymmetric problems of circular plates is presented. The plate is assumed to be linearly elastic, and large rotations and strains are allowed. Shear deformation and changes in the plate thickness are neglected. Equilibrium equations are formulated, and a shooting method is applied to obtain numerical results for plates subjected to a uniform pressure. The edge of the plate is assumed to be either simply supported or clamped, and is free to move radially. The resulting deflections are compared to those based on the von Kármán theory.

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Reissner, E., 1949, “On Finite Deflections of Circular Plates,” Non-Linear Problems in Mechanics of Continua, Proceedings of Symposia in Applied Mathematics, Vol. I, American Mathematical Society, New York, pp. 213–219.
Simmonds, J. G., 1983, “Closed-Form, Axisymmetric Solution of the von Karman Plate Equations for Poisson's Ratio One-Third,” ASME J. Appl. Mech., 50(4), pp. 897–898. [CrossRef]
Frakes, J. P., and Simmonds, J. G., 1985, “Asymptotic Solutions of the von Karman Equations for a Circular Plate Under a Concentrated Load,” ASME J. Appl. Mech., 52(2), pp. 326–330. [CrossRef]
Taber, L. A., 1985, “Nonlinear Asymptotic Solution of the Reissner Plate Equations,” ASME J. Appl. Mech., 52(4), pp. 907–912. [CrossRef]
Brodland, G. W., 1986, “Nonlinear Deformation of Uniformly Loaded Circular Plates,” Solid Mech. Arch., 11(4), pp. 219–256.
Taber, L. A., 1986, “A Variational Principle for Large Axisymmetric Strain of Incompressible Circular Plates,” Int. J. Non-Linear Mech., 21(5), pp. 327–337. [CrossRef]
Taber, L. A., 1987, “Asymptotic Expansions for Large Elastic Strain of a Circular Plate,” Int. J. Solids Struct., 23(6), pp. 719–731. [CrossRef]
Brodland, G. W., 1988, “Highly Non-Linear Deformation of Uniformly-Loaded Circular Plates,” Int. J. Solids Struct., 24(4), pp. 351–362. [CrossRef]
Reissner, E., 1945, “The Effect of Transverse Shear Deformation on the Bending of Elastic Plates,” ASME J. Appl. Mech., 12(2), pp. A68–A77.
Wang, C. M., Lim, G. T., Reddy, J. N., and Lee, K. H., 2001, “Relationships Between Bending Solutions of Reissner and Mindlin Plate Theories,” Eng. Struct., 23(7), pp. 838–849. [CrossRef]
Plaut, R. H., 2009, “Linearly Elastic Annular and Circular Membranes Under Radial, Transverse, and Torsional Loading. Part I: Large Unwrinkled Axisymmetric Deformations,” Acta Mech., 202(1), pp. 79–99. [CrossRef]
Gere, J. M., and Goodno, B. J., 2009, Mechanics of Materials, 7th ed., Cengage Learning, Stamford, CT.
Ozkul, M. H., and Mark, J. E., 1994, “The Effect of Preloading on the Mechanical Properties of Polymeric Foams,” Polym. Eng. Sci., 34(10), pp. 794–798. [CrossRef]
Hochradel, K., Rupitsch, S. J., Sutor, A., Lerch, R., Vu, D. K., and Steinmann, P., 2012, “Dynamic Performance of Dielectric Elastomers Utilized as Acoustic Actuators,” Appl. Phys. A, 107(3), pp. 531–538. [CrossRef]
Schmidt, R., and DaDeppo, D. A., 1975, “On Finite Axisymmetric Deflections of Circular Plates,” Z. Angew. Math. Mech., 55(12), pp. 768–769. [CrossRef]
Way, S., 1934, “Bending of Circular Plates With Large Deflection,” Trans. ASME, 56(8), pp. 627–636.
Chien, W.-Z., 1947, “Large Deflection of a Circular Clamped Plate Under Uniform Pressure,” Acta Phys. Sin., 7(2), pp. 102–113.
Chien, W.-Z., and Yeh, K.-Y., “On the Large Deflection of Circular Plate (in Chinese),” Acta Phys. Sin., 10(3), pp. 209–238.
Timoshenko, S., and Woinowsky-Krieger, S., 1959, Theory of Plates and Shells, 2nd ed., McGraw-Hill, New York.
Chia, C.-Y., 1980, Nonlinear Analysis of Plates, McGraw-Hill, New York.
Jensen, H. M., 1991, “The Blister Test for Interface Toughness Measurement,” Eng. Fract. Mech., 40(3), pp. 475–486. [CrossRef]
Ye., J., 1991, “Large Deflection Analysis of Axisymmetric Circular Plates With Variable Thickness by the Boundary Element Method,” Appl. Math. Model., 15(6), pp. 325–328. [CrossRef]
Cao, J., 1996, “Computer-Extended Perturbation Solution for the Large Deflection of a Circular Plate. Part I: Uniform Loading With Clamped Edge,” Q. J. Appl. Math., 49(2), pp. 163–178. [CrossRef]
Li, Q. S., Liu, J., and Xiao, H. B.2004, “A New Approach for Bending Analysis of Thin Circular Plates With Large Deflection,” Int. J. Mech. Sci., 46(2), pp. 173–180. [CrossRef]
Altekin, M., and Yükseler, R. F., 2011, “Large Deflection Analysis of Clamped Circular Plates,” Proceedings of the World Congress on Engineering (WCE 2011), London, July 6–8.
Striz, A. G., Jang, S. K., and Bert, C. W., 1988, “Nonlinear Bending Analysis of Thin Circular Plates by Differential Quadrature,” Thin-Walled Struct., 6(1), pp. 51–62. [CrossRef]
Chen, Y. Z., and Lee, K. Y., 2003, “Pseudo-Linearization Procedure of Nonlinear Ordinary Differential Equations for Large Deflection Problem of Circular Plates,” Thin-Walled Struct., 41(4), pp. 375–388. [CrossRef]
Chen, Y. Z., 2012, “Innovative Iteration Technique for Nonlinear Ordinary Differential Equations of Large Deflection Problem of Circular Plates,” Mech. Res. Commun., 43(1), pp. 75–79. [CrossRef]


Grahic Jump Location
Fig. 1

Deformed plate segment along a radius

Grahic Jump Location
Fig. 2

Normalized central deflection as function of normalized pressure for clamped and simply supported movable edges, with ν = 0.3; solid curves for GR theory with a/h = 50, dots for von Kármán theory



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