Extended Poisson’s Theory for Analysis of Bending of a Simply Supported Square Plate

International Journal of Civil Engineering
© 2015 by SSRG - IJCE Journal
Volume 2 Issue 11
Year of Publication : 2015
Authors : Kaza Vijayakumar
How to Cite?

Kaza Vijayakumar, "Extended Poisson’s Theory for Analysis of Bending of a Simply Supported Square Plate," SSRG International Journal of Civil Engineering, vol. 2,  no. 11, pp. 1-5, 2015. Crossref, https://doi.org/10.14445/23488352/IJCE-V2I11P101


Nature of solutions from different methods of analysis is examined with reference to exact solution of text book problem of bending of a simply supported square plate under bi-sinusoidal load. Methods of analysis based on stationary property of total potential correspond to plate element equilibrium equations. In these methods, vertical displacement is a domain variable like in 3-D equations of equilibrium in terms of displacements. Aim of the present work is to show that these methods deal with solution of associated torsion problem instead of bending problem. Solution of bending problem is only through methods based on vertical displacement as a face variable.


Plates, Bending, Isotropy, Elasticity.


[1] G Kirchhoff, “Über das Gleichgewicht und die Bewegung einer elastischen Scheibe”, Journal für reins und angewandte Mathematik 40, pp. 51–88, 1850.
[2] H Hencky, “Über die Berücksichtigung der Schubverzerrung in ebenen Platten”, Ingenieur-Archiv 16, pp.72-76, 1947.
[3] E Reissner, “On the theory of bending of elastic plates”, Journal of Mathematics and Physics, 23, pp. 184-191, 1944.
[4] K Vijayakumar, “Modified Kirchhoff’s Theory of Plates Including Transverse Shear Deformations”, Mechanics Research Communications, Vol. 38(3), pp. 2011-2013, 2011.
[5] Y M Ghugal and R P Shimpi, “A Review of Refined Shear Deformation Theories of Isotropic and Anisotropic Laminated Plates”, Journal of Reinforced Plastics and Composites, 21 775, 2002. DOI: 10.1177/073168402128988481
[6] K Vijayakumar, “Review of a few selected theories of plates in bending”, Journal of Applied Mathematics Volume 2014, Article ID 291478, 2014. http://dx.doi.org/10.1155/2014/291478
[7] K Vijayakumar, “A New Look at Kirchhoff's Theory of Plates”, AIIA Journal, 47, pp. 1045- 1046, 2009. DOI: 10.2514/1.38471.
[8] T Lewinski, “On the Twelth-Order Theory of Elastic Plates”, Mech. Res. Comm. 17(6), pp. 375-382, 1990.
[9] S A Ambartsumyan, “On a theory of bending of anisotropic plates”, (in Russian) Izv. Akad.Nauk SSSR Otd.Tekh. Nauk, 5, pp. 69-77, 1958.
[10]T. K. Meghare and P. D. Jadhav, A simple higher order theory for bending analysis of steel beams, SSRG International Journal of Civil Engineering (SSRG-IJCE) ISSN: 2348 – 8352, volume 2, Issue 4,April 2015,pp-31-38.
[11] P. S. Gujar , K. B. Ladhane, Bending Analysis of Simply Supported and Clamped Circular Plate, SSRG International Journal of Civil Engineering (SSRG-IJCE) ISSN: 2348 – 8352, Volume 2 Issue 5,May 2015, pp. 69-75.