Bending Analytic Solutions Of Anisotropic Rectangular Medium-thickness Plate With Four Free Edges On The Different Bearing Forms

Based on the AMapuy MяH’s anisotropic medium-thickness plate theory,it establishes the governing equations of anisotropic medium-thickness plate and the coordination equation under different support which forms a free boundary value problem.It could be expressed by three unknown generalized displacement functions.The problem can be symmetrically decomposed into the superposition of the center symmetric problem and the center anti-symmetric problem.By using the Fourier series method,the partial differential equations are solved into the solution of algebraic equations and the bending analytic solutions of anisotropic rectangular medium thickness plate with four free edges is obtained,including expressions of internal forces of plate and the support reaction force.Then according to MATLAB,the analytical bending solution can be acquired.Finally,the numerical examples are in good agreement with literature,thus to certify the methods in this paper are practical and the theoretical derivation is correct.It has many advantages,which cancels the assumption of straight line,overcomes the difficulty in solving mathematical problems,eliminates the disadvantages of numerical method that makes the solution more practical and fills in gaps of analytical solution of anisotropic medium thick plate.On the different bearing forms,it is concluded that amplitude of deflection and internal force of plate with the influence of plate thickness,foundation plate elastic modulusxE and foundation under horizontal directional elastic modulus ratio1 E,position of supporting points and the number of changes,coefficient curve support,anisotropy.This method not only can be used to study the bending properties of anisotropic rectangular plate,but also to analyze the dynamic characteristics of anisotropic rectangular plates with different boundary constraints.