Galerkin Method For Bending Problems Of Rectangular Plate Based On Generalized Winkler Foundation

In analysis of many engineering structures or components, such as, airport runway,dock floor of raft foundation, etc., it can be simplified as the analysis and calculationbased on the elastic foundation plate. The Galerkin solution for the bending problems ofthe free rectangular plate which is based on the generalized Winkler foundation,described in this paper, is the complementarity for the theoretical investigation of theelastic foundation plate, also has important therotical significance for solving practicalengineering problems.According to the relevant literature and information about the previous studies ofgeneralized Winkler foundation, the research goal of this paper is to find one deflectionfunction which can satisfy the condition of the four-edge free boundary of therectangular plate, establish a new sheet of equation based on the generalized Winklermodel, complete the derivation of the formular by using Galerkin method, thencalculate the numerical solution by program. Based on the comparation between thecalculation examples and the results of this paper, prove the correctness of the methodand the differences of calculation examples for the deflection function of the rectangularplate four-edge free boundary based on such foundation model. The paper foucuses onthe parameters changes on the generalized Winkler foundation, the impact on the platebending, and the convergence of the functions, etc.The results show that the variational method has good convergence and accuracy.When the difference of the subgrade bed coefficient is large, the difference between theWinkler plate bending and the generalized Winkler plate bending will be large, thisshould be paid attention to. When the conditions and other factors are same, with theincrease of the external loads, the difference of the center deflection between thegeneralized Winkler foundation plate and the Winkler foundation plate is obviouse. So for the practical engineering case, cannot ignore the monlinear factors of the foundationwhen the external loads value is large. With increasing loading zone or decreasingsubgrade bed coefficient, plate deflection and bending moment will increase. Platedefection will decrease and bending moment will increase if the plate thickness ration isincreasing.The theory of this variational method is clear, the method is simple andconvenient. It has a broad application prospect for of practical engineering cases. Thedeflection function can not only be fully used on the static problem of four-edge freesheet, but also can be applied as mathematical model for the further research of freevibration and stability.