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Exact Elasticity Solution for Axisymmetric Deformation of Circular Plates

  • W.-D. Tseng (a1) and J.-Q. Tarn (a2)

Abstract

We present an exact analysis of axisymmetric bending of circular plates according to elasticity theory. On the basis of Hamiltonian state space approach, a rigorous solution of the problem is determined by means of separation of variables and symplectic eigenfunction expansion in a systematic way. The thickness effect on bending of circular plates and the applicability of the classical plate solutions for the problem are evaluated accordingly.

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*Corresponding author (wdtseng1125@gmail.com)

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1.Timoshenko, S. P. and Woinowsky-Krieger, S., Theory of Plates and Shells, 2nd Ed., McGraw-Hill, New York (1959).
2.Love, A. E. H., The Mechanical Theory of Elasticity, 4th Ed., Cambridge University Press, Cambridge (1927).
3.Reissner, E., “The Effect of Transverse Shear Deformation on the Bending of Elastic Plates,” Journal of Applied Mechanics, 67, pp. A-69 (1945).
4.Reissner, E., “On Bending of Elastic Plates,Quarterly of Applied Mathematics, 5, pp. 5568 (1947).
5.Ambartsumyan, S. A., Theory of Anisotropic Plates, Technomic Publishing, Chicago (1970).
6.Speare, P. R. S., “Shear Deformation in Elastic Beams and Plates,” Ph.D. Dissertation, University of London, U.K. (1975).
7.Timoshenko, S. P. and Goodier, J. N., Theory of Elasticity, 3rd Ed., McGraw-Hill, New York (1970).
8.Tarn, J. Q., A State Space Formalism for Anisotropic Elasticity, Part II: Cylindrical Anisotropy, International Journal of Solids and Structures, 39, pp. 51575172 (2002).
9.Meleshko, V. V. and Tokovyy Yu, V., “Equilibrium of an Elastic Finite Cylinder under Axisymmetric Discontinuous Normal Loadings,” Journal of EngineeringMathematics, 78, pp. 143166 (2013).
10.Valov, G. M., “On the Axially-symmetric Deformations of a Solid Circular Cylinder of Finite Length,” Journal of Applied Mathematics and Mechanics, 26, pp. 975999 (1962).
11.Shibahara, M. and Oda, J., “Problems on the Finite Hollow Cylinders under the Axially Symmetrical Deformations,” Bulletin of JSME, 11, pp. 10001014. (1968).
12.Chau, K. T. and Wei, X. X., “Finite Solid Circular Cylinders Subjected to Arbitrary Surface Load, Part I—Analytic Solution,” International Journal of Solids and Structures, 37, pp. 57075732 (2000).
13.Meleshko, V V., “Equilibrium of an Elastic Finite Cylinder: Filon’s Problem Revisited,” Journal of Engineering Mathematics, 46, pp. 355376 (2003).
14.Tokovyy, Yu V., “Reduction of a Three-dimensional Elasticity Problem for a Finite-Length Solid Cylinder to the Solution of Systems of Linear Algebraic Equations,” Journal of Mathematical Sciences, 190, pp. 683696 (2013).
15.Tarn, J. Q., Tseng, W. D., and Chang, H. H., “A Circular Elastic Cylinder under Its Own Weight,” International Journal of Solids and Structures, 46, pp. 28862896 (2009).
16.Hildebrand, F. B., Advanced Calculus for Applications, 2nd Ed., Prentice-Hall, Englewood Cliffs, New Jersey (1976).
17.Zhong, W. X., A New Systematic Methodology for Theory of Elasticity, Dalian University of Technology Press, Dalian, China (1995) (in Chinese).
18.Hildebrand, F. B., Methods of Applied Mathematics, 2nd Ed., Prentice-Hall, Englewood Cliffs, New Jersey (1965).
19.Tarn, J. Q. and Chang, H. H., “A Refined State Space Formalism for Piezothermoelasticity,” International Journal of Solids and Structures, 45, pp. 30213032 (2008).

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