The Bending Of Moderately Rectangular Orthotropic Thick Plates With Four Free Edges On The Elastic Foundation

In this paper, basing on Hu Haichang's bending theory of flat plate with extensive three-displacement, which considering shear deformation, the governing differential equations are derived from moderately rectangular orthotropic thick plates with four free edges on the elastic foundation. And using double Fourier Series ,the exact solution for it is discussed in detail.In order to solve this problem, double Fourier Series is used in the boundary conditions of free edges. Virtual load method is be used so that the displacement satisfies all terms of boundaries and corners .And using symmetry ,the arbitrary loading and displacement are divided into four circumstances .According to the rule of adding theory ,the governing equation and the boundary conditions are divied. At the time, they are expanded indouble Fourier series. So the governing partial differential equations were reduced to a series of algebraic eqution. Finally, the exact solution is derived. And the author successfully solve the bending problems of moderately rectangular orthotropic think plates with four free edges on the elastic foundation.Because of using double Fourier Series, the development of equations is very simple, and the answer has the advantages of uniform mathematic examples are worked out by using MATLAB, and some distortion graphics are given under different cases .It is easy to contrast and check.The way and the results in this paper puts forward bending theory of flat plate. Also it is helpful and practical for the design and construction of expressway, airport aircraft parking area, wharf freight shed and plate type foundation.