Four Edges Free Plates On Winkler Foundation With Galerkin Solution

Linear foundation plate bending solution only solves part of the problem of staticinteraction between the foundation and the basis of research areas, and the nonlinearelastic foundation is still part of the research can not be solved. In practical engineering,soil often exhibit non-linear characteristics, to study the issue with a traditional Winklerfoundation model will a big difference with the actual situation. Therefore, this paperuse the non-linear Winkler foundation model to solve the problem of Four edges FreePlates.Under Small Deflection plate bending theory based on the linear Winklerfoundation raft foundation board into a nonlinear elastic plate on Winkler. According tothe balance between the curved plate bending can effectively reflect the establishmentof the non-linear differential equations of non-linear elastic foundation with foundationplate match the actual work of the four sides of rectangular plates, the freedom to selecta set of boundary conditions to meet the four sides of the deflection function,using theGalerkin solving the four sides of rectangular plates on nonlinear elastic foundationsproblem.The combination of these specific forms of equations using mathematicalprogramming software Matlab numerical calculation and analysis.Comparative Throughliterature examples, analysis this article rectangular plate bending problem ofconvergence; Finally, the comparison with the literature study, learn under thefoundations of linear and nonlinear elastic foundation case elastic rectangular platedeflection and internal forces differences.The results showed that, Galerkin method advantage of rapid convergence andaccuracy better; When using piecewise non-linear way to fit the actual soil profile, there are differences between linear elastic foundation and nonlinear elastic foundation,towhich much attention should be paid in the design. With the increase in size of load,load increasing,one thing that is clear is that rectangular plate deflection and bendingmoments have seen very different of impact. The analytical method of this paper has ageneral sense, theoretical basis of this paper can be used to solve the four sides ofrectangular plates on linear and nonlinear elastic foundations problem,The resultsobtained can be used for reference in engineering practice.