The Bending Of Circular Plate On Transversrly Isotropic Two-parameter Elastic Foundation

In practical engineering application,many existing structures can be simplified as the deformation of plate on elastic foundation.Therefore,it is of great significance to research the plate on elastic foundation.The existing elastic foundation models include Winkler foundation model,two-parameter elastic foundation model and elastic continuum foundation model.Among them,the two-parameter foundation model has irreplaceable advantages.In the previous study of the two-parameter foundation model,most scholars believe that the foundation is continuous,linear elastic,uniform and isotropic.But the test shows that many foundations are closer to the transverse isotropy.Its horizontal direction can be regarded as isotropic,but the properties of foundation soil along the vertical direction are quite different.Therefore,the research on transversely isotropic two-parameter foundation is an important supplement to the two-parameter foundation.In this paper,on the basis of the principle of minimum potential energy,the variational method is adopted to deduce the governing equations and boundary conditions of elastic circular plate on the transversrly isotropic two-parameter elastic foundation.It is very important to choose the appropriate deflection function for the study of the bending of circular plate on elastic foundation.In this paper,Fourier-Bessel series method is selected to study the bending problem of circular plates on transverse isotropic two-parameter foundation model.This method is not only applicable to all kinds of loads,but also overcomes the shortcoming of discontinuity in boundary conditions when not all edges are simply supported.And on this basis,for the problem of how to determine attenuation parameters?,the conditions for the parameters are determined according to the Vlazov model.And the relatively reliable attenuation parameters are obtained by iterative method.The defect of direct selection of attenuation parameters in two-parameter model is improved.In this paper,the deformation of a circular plate on a transversely isotropic two-parameter foundation is obtained by theoretical derivation and mathematical software programming.The influence of different foundation parameters on deformation is analyzed.The calculation results show that the modulus of elasticity in transversely isotropic plane E_s1,the modulus of elasticity in vertical transverse isotropic plane E_s2,the modulus of elasticity of plate E and the thickness of the soil H both have some influence on attenuation parameters?and foundation reaction coefficient k.The influence of soil thickness H is relatively large,while the influence of elastic modulus E of the plate is very small,which can be basically ignored.However,the magnitude of the load does not affect the attenuation parameter?and the foundation reaction coefficient k.