General Solution of Thick Plates on Winkler-Pasternak Foundation Using Orthogonal Polynomial Displacement Functions

Abstract

A solution for thick plates on Winkler-Pasternak foundation using characteristic orthogonal polynomials (COPs) displacement functions was presented in this study. A shear deformation function was developed from Soldatos’ (1992) trigonometric function and the Ritz energy approach was used to determine the total potential energy of the thick plate on elastic foundation. This method presents a simple and efficient method where only definite integration is required to obtain solutions. Results for non-dimensional in-plane and out-of-plane displacements for simply supported (SSSS) thick plates were presented and was observed to converge with that of other third-order shear deformation theories (TSDT) available in literature. From the study, it was observed that the in-plane and out-of-plane displacements reduced generally as the foundation modulus of the soil increased and decreases as the span-depth ratio increased for each aspect ratio. Both the Winkler and Pasternak foundation parameters influenced the results obtained as the foundation modulus is dependent on these parameters.