Exact Solution Of Anisotropic Rectangular Plates On Elastic Foundation With Four Even Free

In this paper, from the basic equations of the anisotropic rectangular plate with four free edges on elastic foundation, the exact solution for it is discussed indetail.Using symmetry, the arbitrary loading and displacement are divided intofour circumstances. According to the rule of adding theory, the governingequations are divided. That is, a four-order partial differential equation is turnedto two four-order partial differential equation teams, which are one eight-orderpartial differential equation in essence. So the problem of anisotropic plate'sexact solution is well solved eventually. Additional, in this paper, doubleFourier Series is used to solve the problems of free edges. Virtual load methodis be used so that the displacement satisfies all terms of boundaries andcorners. The exact solution can be derived from the final divided governingequations and boundary conditions.Because of using double Fourier Series, the development of equations isvery simple, and the answer has the advantages of uniform mathematic expression and easily drawing-up calculating program. Several numerical examples are worked out by using MATLAB, and some distortion graphics are given under different cases. It is easy to contrast and check.Obviously, the results of the present paper have important meaning not onlyin enriching the theory of the plate, but also in the application of engineeringpractice.