Research Papers

Theoretical Solution for Thick Plate Resting on Pasternak Foundation by Symplectic Geometry Method

[+] Author and Article Information
Liu Heng

School of Civil and Hydraulic Engineering,
Dalian University of Technology,
Dalian 116024, China

Manuscript received March 26, 2013; final manuscript received June 8, 2013; accepted manuscript posted June 13, 2013; published online September 18, 2013. Editor: Yonggang Huang.

J. Appl. Mech 81(3), 031007 (Sep 18, 2013) (4 pages) Paper No: JAM-13-1135; doi: 10.1115/1.4024797 History: Received March 26, 2013; Revised June 08, 2013; Accepted June 13, 2013

Based on the analogy of structural mechanics and optimal control, the theory of the Hamilton system can be applied in the analysis of problem solving using the theory of elasticity and in the solution of elliptic partial differential equations. With this technique, this paper derives the theoretical solution for a thick rectangular plate with four free edges supported on a Pasternak foundation by the variable separation method. In this method, the governing equation of the thick plate was first transformed into state equations in the Hamilton space. The theoretical solution of this problem was next obtained by applying the method of variable separation based on the Hamilton system. Compared with traditional theoretical solutions for rectangular plates, this method has the advantage of not having to assume the form of deflection functions in the solution process. Numerical examples are presented to verify the validity of the proposed solution method.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Westergaard, H. M., 1926, “Stresses in Concrete Pavements Computed by Theoretical Analysis,” Public Roads, 7(2), pp. 25–35.
Zhu, J. M., 1995, “CC Series Solution for Bending of Rectangular Plates on Elastic Foundation,” Appl. Math. Mech., 16, pp. 593–601. [CrossRef]
Wang, K. L., and HuangY., 1986, “Thick Rectangular Plates With Four Free Edges on Elastic Foundation,” Acta Mech. Solida Sin., 1, pp. 37–49 (in Chinese).
Shi, X., and Yao, Z., 1989, “The Solution of a Rectangular Thick Plate With Free Edges on a Pasternak Foundation,” J. Tongji University, 17(2), pp. 173–184 (in Chinese).
Fwa, T. F., Shi, X. P., and Tan, S. A., 1996, “Analysis of Concrete Pavements by Rectangular Thick-Plate Model,” J. Transp. Eng., 122(2), pp. 146–154. [CrossRef]
Li, R., Zhong, Y., and Tian, B., 2011, “On New Symplectic Superposition Method for Exact Bending Solutions of Rectangular Cantilever Thin Plates,” Mech. Res. Commun., 38, pp. 111–116. [CrossRef]
Li, R., Zhong, Y., and Li, M., 2013, “Analytic Bending Solutions of Free Rectangular Thin Plates Resting on Elastic Foundations by a New Symplectic Superposition Method,” Proc. R. Soc. A, Math. Phys. Eng. Sci., 469(2153), p. 20120681. [CrossRef]
Huang, Y. H., 1974, “Finite Element Analysis of Slabs on an Elastic Solids,” J. Transp. Eng. Div., 100(2), pp. 403–416.
Tabatabaie, A. M., and Barenberg, E. J., 1980, “Structural Analysis of Concrete Pavement Systems,” Transp. Eng. J., 106(5), pp. 493–506.
Zhong, W., 1995, A New Systematic Methodology for Theory of Elasticity, Dalian University of Technology Press, Dalian, China (in Chinese).
Hu, H. C., 1981, Variational Principle in Elasticity and Its Applications, Science Press, Beijing (in Chinese).
Zhong, Y., Li, R., Liu, Y., and Tian, B., 2009, “On New Symplectic Approach for Exact Bending Solutions of Moderately Thick Rectangular Plates With Two Opposite Edges Simply Supported,” Int. J. Solids Struct., 46, pp. 2506–2513. [CrossRef]
Yao, W., and Zhong, W., 2002, Symplectic Elasticity, Higher Education Press, Beijing (in Chinese).


Grahic Jump Location
Fig. 1

A thick plate with four free edges



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In