Bending Of Plate Resting On Non-uniform Elastic Foundation

The bending of plate resting on non-uniform elastic foundation is a supplement forthe research field of interaction between ground and foundation, being a very importantscientific research value and application value. In the present study, the bending of platewith four free edges resting on non-uniform Winkler foundation is discussed.The raft foundation is modeled as a elastic thin plate resting on non-uniformWinkler foundation, the mechanics equations for bending of a rectangular plate areestablished, the displacement function for meeting the boundary conditions is selected,Ritz Method, Modified Ritz Method and Galerkin Method are used to analyze thebending of plate resting on non-uniform Winkler foundation, giving the deflection andbending moment for the bending of rectangular plate with four free edges under lateralloads.Combined with the specific form of algebraic equations, using mathematicalsoftware Matlab programming numerical analysis. Firstly, discussing the convergencewith the bending problem of rectangular plate; secondly, analysis the differences ofrectangular plate deflection and bending moment which on uniform foundation and onnon-uniform foundation; finally, analysis the influence of the non-uniform foundationarea, the fonudation coefficient, the plate side-to-thickness ratio and the area of loads tobending of rectangular plate.The results show that the convergence and the precision of Galerkin Method is thebest, Modified Ritz Method is the second, Ritz Method is the slowest; and when thefonudation coefficient k1and k2have great differences, the bending of plate on uniformfoundation and the bending of plate on non-uniform foundation have obviousdifferences, those differences should be paid attention in the designs of plate; with thecenter area, the area of loads increase, the deflection and bending moment of therectangular plate are increasing constantly; in the center area of the same premise, along with the central region fonudation coefficient constantly decreases, the deflection andbending moment of the rectangular plate are increasing constantly; with the plateside-to-thickness ratio increase, the deflection of the rectangular plate are increasingconstantly, the bending moment in turn decreased.The analytic method of this paper has a general sense, the theoretical basis of thispaper can be used to analysis the bending problem of rectangular plate with four freeedges resting on non-uniform elastic foundation, also can be analyzed the problem ofplate resting on elastic foundation with various boundary conditions, the conclusion ofthis paper will give better understanding for engineering design.