Analytical solution to the elastic bending of long and rectangular thin plate resting on rubber foundation

In this study, the elastic bending of long and rectangular plate resting on unilateral rubber foundation under a concentrated load has been investigated. A new continuum model has been developed to study the rubber foundation reaction. A simplified one-parameter model could thus be obtained for the foundation reaction permitting the parameter to be directly determined without resorting to trial estimation. The governing differential equations have been derived for the plate–foundation system. A numerical–analytical method has been proposed for the exact and closed-form solution of the equations. Several examples have been presented in order to draw a comparison between the results of the proposed solution and the conventional numerical solution. The results have also been compared with the Winkler's mechanical model. Finally, the effect of various parameters on the behaviour of the plate–foundation system has been studied. The results indicate that the length of contact region between the plate and the foundation is influenced by the mechanical and geometrical parameters of the plate and also on the foundation modulus but does not depend on the loading.