Keywords: deflections, elastic foundations, finite difference, large rectangular plates.

A large deflection analysis is presented for thin and thick plates [1,2] with simply supported and fixed edges subjected to a transverse distributed load and resting on an elastic foundations. In the present study, the Winkler model is used to model the elastic foundations. This model assumes the soil medium to consist of a system of independent spring elements. The displacement occurs immediately under the loaded area and outside this region; the displacement is zero

The basic or governing equations for thin and thick plates with large deflections are derived. The finite difference technique [3] is used in the analysis using the computer program (FDAPEF) (finite difference analysis of plates on elastic foundations). The program solves the problem of simply supported and fixed plate edges. The governing differential equations of thick plate on an elastic foundation are converted into finite differences. An assembly of the system of simultaneous algebraic equations is made. The Gauss Jordan method is used in the program to solve the system of equations and obtain deflections and rotations at each node. The deflections obtained are compared with deflections of the previous iteration and the procedure repeated until convergence is obtained. The analysis is nonlinear. Comparison between the results obtained by the present analysis and those obtained by other investigations [4,5] are made. The present analysis shows satisfactory results when compared with those obtained by other studies with percentage difference of 2.7% in the value of the deflection value.

Typical results are presented in dimensionless graphical form for different parameters and loading conditions. Several important parameters are incorporated in the analysis to study for example the effect of the vertical subgrade reaction, plate thickness and the Poisson's ratio on deflections and bending moments.

From this study, many conclusions are obtained. The comparison between small and large deflection theory shows a considerable difference for thin plates, while the difference for thick plates is very small because the effect of the large deflection term in the basic equation vanishes when the thickness increases.

The effect of increasing Poisson's ratio for large deflections will decrease the central deflection and increase the resistance moment because it increases the flexural rigidly of the plate. The deflections and moments at the centre of thick plates on an elastic foundation are reduced with increasing of the vertical subgrade reactions because the foundation stiffness increases. The effect of increasing thickness in large deflection theory for thick plates shows that the deflection at the centre decreased and the resistant moment at the centre increased as the value of the thickness was increased because of increasing the flexural rigidity of the plate.

1

E. Reissner, "The Effect of Transverse Shear Deformation on the Bending of Elastic Plates", American Society of Mechanical Engineers, Journal of Applied Mechanics, 12, 69-77, 1945.

2

R. Mindlin, "Influence of Rotatory Inertia and Shear on Flexural Motions of Isotropic Elastic Plates", American Society of Mechanical Engineers, Journal of Applied Mechanics, 18, 31-38, 1951.

3

A.W. Al-Khafaji, J.R. Tooley, "Numerical Methods in Engineering Practice", CBS College Publishing, New York, 1986.

4

M.H. Al-Allaf, "Three Dimensional Finite Element Analysis of Thick Plates on Elastic Foundations", M.Sc. Thesis, Faculty of Engineering, Al-Nahrain University, Baghdad, Iraq, 2005.

5

S. Timoshenko, S. Woinowsky-Krieger, "Theory of Plates and Shells", McGraw-Hill, New York, 1959.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £95 +P&P)