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Exact Elasticity Solution for Axisymmetric Deformation of Circular Plates

Published online by Cambridge University Press:  15 July 2015

W.-D. Tseng  and
J.-Q. Tarn
W.-D. Tseng*
Affiliation:
Department of Construction Engineering, Nan Jeon University of Science and Technology, Tainan, Taiwan
J.-Q. Tarn
Affiliation:
Department of Civil Engineering, National Cheng Kung University, Tainan, Taiwan
*
*Corresponding author ([email protected])
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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.

Keywords

Circular platesState spaceThickness effectThree-dimensional elasticity
Type
Research Article
Information
Journal of Mechanics , Volume 31 , Issue 6 , December 2015 , pp. 617 - 629
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2015 

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References

REFERENCES

1.Timoshenko, S. P. and Woinowsky-Krieger, S., Theory of Plates and Shells, 2nd Ed., McGraw-Hill, New York (1959).Google Scholar
2.Love, A. E. H., The Mechanical Theory of Elasticity, 4th Ed., Cambridge University Press, Cambridge (1927).Google Scholar
3.Reissner, E., “The Effect of Transverse Shear Deformation on the Bending of Elastic Plates,” Journal of Applied Mechanics, 67, pp. A-69 (1945).Google Scholar
4.Reissner, E., “On Bending of Elastic Plates,” Quarterly of Applied Mathematics, 5, pp. 55–68 (1947).CrossRefGoogle Scholar
5.Ambartsumyan, S. A., Theory of Anisotropic Plates, Technomic Publishing, Chicago (1970).Google Scholar
6.Speare, P. R. S., “Shear Deformation in Elastic Beams and Plates,” Ph.D. Dissertation, University of London, U.K. (1975).Google Scholar
7.Timoshenko, S. P. and Goodier, J. N., Theory of Elasticity, 3rd Ed., McGraw-Hill, New York (1970).Google Scholar
8.Tarn, J. Q., A State Space Formalism for Anisotropic Elasticity, Part II: Cylindrical Anisotropy, International Journal of Solids and Structures, 39, pp. 5157–5172 (2002).Google Scholar
9.Meleshko, V. V. and Tokovyy Yu, V., “Equilibrium of an Elastic Finite Cylinder under Axisymmetric Discontinuous Normal Loadings,” Journal of EngineeringMathematics, 78, pp. 143–166 (2013).Google Scholar
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. 975–999 (1962).Google Scholar
11.Shibahara, M. and Oda, J., “Problems on the Finite Hollow Cylinders under the Axially Symmetrical Deformations,” Bulletin of JSME, 11, pp. 1000–1014. (1968).CrossRefGoogle Scholar
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. 5707–5732 (2000).CrossRefGoogle Scholar
13.Meleshko, V V., “Equilibrium of an Elastic Finite Cylinder: Filon’s Problem Revisited,” Journal of Engineering Mathematics, 46, pp. 355–376 (2003).Google Scholar
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. 683–696 (2013).Google Scholar
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. 2886–2896 (2009).Google Scholar
16.Hildebrand, F. B., Advanced Calculus for Applications, 2nd Ed., Prentice-Hall, Englewood Cliffs, New Jersey (1976).Google Scholar
17.Zhong, W. X., A New Systematic Methodology for Theory of Elasticity, Dalian University of Technology Press, Dalian, China (1995) (in Chinese).Google Scholar
18.Hildebrand, F. B., Methods of Applied Mathematics, 2nd Ed., Prentice-Hall, Englewood Cliffs, New Jersey (1965).Google Scholar
19.Tarn, J. Q. and Chang, H. H., “A Refined State Space Formalism for Piezothermoelasticity,” International Journal of Solids and Structures, 45, pp. 3021–3032 (2008).Google Scholar