Variational Solutions Of The Moderately Thick Rectangular Plates With Four Edges Free On The Elastic Half-space Foundation

The rectangular plates on elastic foundation with four edges free have an extensive application in manufacture in the project. The theory of moderately thick plate on elastic foundation is often applied in the practical project to calculate and analyze thicker elastic foundation plates in the actual project. This paper researched the variational solutions of the moderately thick rectangular plates with four edges free on the elastic half space foundation.The commonly used calculation models of analysis of soil-structure interaction are: Winkler foundation, double parameters foundation and elastic half space foundation. The advantage of Winkler foundation is its simple calculation. However this model has conspicuous fault in depict of the access of actual soil, which the Winkler foundation's displacement occurred in areas that was subjected to loading. Double parameters foundation describes the character of foundation soil by two parameters. Although improving the Winkler foundation's inconsistent characters, double parameters foundation has mathematical problem for using two parameters. This paper used elastic half space foundation. This kind of model had considered pressure diffusion, is more reasonable in theory than anther two modals.Based on the bending theory of flat plate with extensive three displacement, this paper used the energy variation method to calculate and analyze the moderately thick rectangular plates problem with four edges free on the elastic half-space foundation. Considering the assuming wholly adhesive friction contact between foundation and rectangle plates, the power series is used as trial function to deduce total energy expression of the moderately thick plates and the elastic half-space foundation according to the theory of three dimensional elastic mechanics, then obtain indeterminate coefficient of trial function by variation method. Finally, the obtained coefficients are introduced into the internal force expression of moderately thick plates theory to solve the moderately thick rectangular plates problem with four free edges on the elastic half-space foundation.This method is simple and easy to put into practice. The result is concise, easy to calculate by computer program and content with boundary conditions. It has a significant instructional meaning of designing and constructing the engineering practices, such as expressway slab, aircraft parking area, dock cargo hold, plate type ground, and so on.