The Bending Of Thick Rectangular Plates With Four Free Edges On The Elastic Half-space Foundation

In this paper the accurate solution for the thick rectangular plates with four free edges laid on elastic half-space foundation is presented., which is based on the Reissner's thick plate theory and stationary displacement's integral calculus solution about the elastic half-space foundation that was subjected to arbitrary loading on the erect axis. The superposition method of single-trigonometric series and double-trigonometric series is used.The accurate solution of rectangular plate with four free edges on the elastic foundation was only presented about simple models, such models as wrinkle foundation and double-parameter foundation, for complex controlled equations. However, wrinkle foundation model has conspicuous fault in depict of the access of actual soil, which the wrinkle foundation's displacement occurred in areas that was subjected to loading. Double-parameter foundation is used two single parameters to describe soil's characters. Although improving the wrinkle foundation's inconsistent characters, double-parameter foundation has mathematical problems for using two parameters. This paper used elastic half-space foundation model, first combined foundation's negative force and plate's loading, then induced thick plate inner-forces expressions from simplified equable equations, at last worked out the accurate solution of rectangular plate with four free edges on elastic foundation using the condition that the displacement of foundation and the displacement of plate is equal on touching plane.The inner-forces expressions became very simple for using Fourier Series and reducing the parameters on the equations , and the problems about elastic half-space became simple for using the condition that the displacement of foundation and the displacement of plate is equal on touching plane. At the same time the conclusion has the advantages of uniform mathematic expressions, are easily worked out by using MATLAB.The method and the conclusion in this paper avoid the complexity of calculation on the elastic half-space foundation and avoid the errors in other foundations. So it has practical meaning and instructive meaning .