The Analytical Solution Of Interaction Between Adjacent Rectangular Plates On Layered Transverse Isotropic Foundation

As the density of urban buildings increases,the space between adjacent buildings decreases.Therefore,the interaction between adjacent building foundations becomes a problem worth studying.Existing studies focus either on a single foundation plate or only study the bending problem of ad jacent plates without considering the stratification of the foundation.In short,there are almost no analytical solutions to the problems studied in this paper.In view of the urgent need in engineering,the interaction between adjacent rectangular plates on layered transverse isotropic foundation is studied in depth.Based on the transversely isotropic foundation solution,the layered foundation solution with load acting on the foundation surface including vertical displacement is obtained by using matrix transfer technique.The integral coordinate system is established on the foundation,and the local coordinate system is established on each board.The transformation relationship between the global coordinate system and the local coordinate system is used to obtain the functional expression of the vertical displacement of the foundation.Using the displacement coordination condition between the plates and the foundation,the deformation coordination equation between the plates and the foundation is established.The governing equation of the plates in parallel and the boundary condition and the corner point condition are established.Finally,the singularity,oscillation function infinite integral technology and Matlab software are used to compile the calculation program.Furthermore,the influence of the calculated depth of the foundation,the spacing between adjacent rectangular plates,the elastic modulus ratio of the foundation and the plate,the elastic modulus ratio of the two plates,the load type and the ratio of the two plates' applied loads on the deflection,internal force and foundation reaction are analyzed through examples.Then,the relationship between the intensity of the interaction between adjacent rectangular plates under vertical harmonic load and the elastic modulus ratio of the foundation,the thickness to width ratio of the plates,the elastic modulus ratio of the two plates and the load ratio of the two plates is discussed.When the adjacent rectangular plates on the layered transverse isotropic foundation are subjected to the vertical static load,the following results can be obtained: as the calculation depth of the foundation increases,the interaction between the two plates becomes increasingly intensified;As the distance increases,the interaction between them decreases.When the two plates act on concentrated load,the deflection of the plate decreases slightly with the increase of the distance between the two plates,so the interaction between the two plates decreases constantly.With the increase of elastic modulus ratio between the foundation and the plate,the interaction between the two plates also increases.With the increase of the elastic modulus ratio of the two plates,the interaction between the two plates increases.With the increase of the load ratio of two plates,the intensity of the interaction between two plates is also increasing.When the adjacent rectangular plates on the layered transverse isotropic foundation are subjected to the vertical simple co-load,we obtain that: with the constant increase of the elastic modulus ratio between the foundation and the plate,the interaction between the two adjacent plates is continuously enhanced;With the decrease of elastic modulus ratio between the first plate and the seco nd plate,the interaction between the two plates is also weakened.As the ratio of thickness to width of two plates decreases,the interaction between two plates intensifies.With the decrease of the load ratio of the two plates,the intensity of the interaction between the two plates increases.The analytical solution in this paper is more consistent with the actual distribution law because the stratification of foundation is considered.