The Bending Of The Rectangular Plate With Four Free Edges When The Plate Is In Non-smooth Contact With The Two-parameter Foundation

Elastic foundation plate is widely used in building engineering.It is the basic component of road,runway and high-rise building foundation.It is very important that these components be used reasonably and safely in engineering practice.In order to study the practical problems of elastic foundation plate in engineering,scholars put forward the corresponding elastic foundation plate model.Many scholars have made a thorough study and formed a relatively complete theoretical system.The existing elastic foundation models can be divided into many kinds according to their simplified ways,and each has its own characteristics,among which the two-parameter foundation model has the advantages of simple mathematical treatment and perfect theory.Therefore,based on the advantages and disadvantages of various elastic foundations,this paper chooses to simplify the foundation into a two-parameter elastic foundation.In this paper,the bending problem of four-sided free rectangular plate in non-smooth contact between plate and two-parameter foundation is studied,which is a supplement to the research field of foundation and structure under static action and can be used as an important reference in practical engineering.In this paper,the bending problem of rectangular plate with four sides is studied.First,by using the principle of minimum potential energy,the variation of potential energy of the whole system of rectangular thin plate,foundation and load is obtained.Then select a deflection function which can satisfy the boundary conditions of four free edges and four free corner points,and solve the problem by simultaneous equations.In this paper,by using the Fourier series method,the trial function to take supplementary item of the form of double trigonometric functions,using Matlab software programming calculation,through iterative solution had attenuation parameters,and then get the foundation reaction coefficient and shear coefficient,finally obtaining plate with double parameters foundation nonsmooth contact with four edges free rectangular thin plate bending deflection and bending moment value,through the comparison,examples and references to prove the rationality and accuracy of the proposed method,the analysis when the plate and the foundation of nonsmooth contact friction factor,the foundation elastic modulus,thickness of foundation,plate thickness,the loading effect on the attenuation parameter and plate bending.In this paper,through rigorous theoretical derivation and Matlab programming solution,the analytic solution of the bending of the four-sided free rectangular thin plate in non-smooth contact between the plate and the two-parameter foundation is obtained,and the influence of each parameter on the attenuation parameter of the foundation and the plate bending is analyzed.Double Fourier series method has the advantages of clear and perfect theory,simple and accurate method and wide application in mechanics.This theoretical method has a strong applicability to the analysis of the interaction between rectangular thin plate and elastic foundation and has a broad application prospect.