The Bending Of Rectangular Thin Plate With Four Free Edges On The Transversely Isotropic Two-parameter Elastic Foundation

As one of common structure form,the plate on elastic foundation has been widely applied in engineering practice.Therefore,it is very important to have an accurate analysis about the model.But transversely isotropic body,which will be more reasonable,is considered for the purpose of simplification and due to the experimental evidence.Most of the previous research is based on the famous Winkler model in spite of the disclosure of inconsistencies.The two parameter foundation model has its own unique characteristics.But how to select the parameter is a key issue,which has been a great obstacle to the further extension of the two-parameter foundation model.The behavior of the plate is influenced by the foundation,and the behavior of the soil is affected by the plate under external loads.The paper is a supplement for the research field of interaction between ground and foundation.Plates and foundations were discussed as a whole system.The article completed the basic theory of plates by the principle of minimal potential energy.The governing equations and the boundary conditions were given.The key to analyze static problems of plate on elastic foundation was to find a suitable deflection function,and we could figure it out with corresponding methods.Ritz Method,Modified Ritz Method and Trigonometric series method and general solution of Fourier series with supplementary terms were used to analyze the bending of plate resting on the foundation,giving the deflection and bending moment for the bending of rectangular plate with four free edges under lateral loads.At the same time,the equation of the attenuated parameter of thefoundation plate was derived.Then the iterative method was used to solve the attenuation parameter and determine the two parameters simultaneously,which solved a key issue for the two-parameter elastic foundation model.In this paper,the refined model mentioned above is studied by using the rigorous mathematical theory and Matlab programming.At last the results indicate that the series are of quick convergence rate.Subgrade coefficient and shear stiffness can be obtained by iteration method instead of the empirical or experimental evaluation of the parameters,which solves the problem that the parameters of the transversely isotropic two-parameter elastic foundation can not be determined.Compared to other literature,the results are coincident.The method has some universality for analyzing the interaction between thin rectangular plate and elastic foundation.The conclusion of this paper will give better understanding for engineering design and provide more practical value.