Expanded Galerkin Method In The Bending Of Moderately Rectangular Orthotropic Thick Plates

In this paper,basing onAMσapμyMRH bending theory of moderately rectangular orthotropic thick plates,galerkin method is expanded,with double cosine series the bending problem of moderately rectangular orthotropic thick plate under various boundaries conditions are analyzed and solved.In ordinary,when the solution of equation are set in,they must simultaneously satisfy displacement boundary conditions and stress boundary conditions,galerkin method used in this paper is the process that on the solution of equation can not satisfy all boundary conditions,only can satisfy partial boundary conditions,they are set in double cosine series,according to petro-galerkin method theory differential equations are processed into algebraic equation.,with the integral conversion of displacement boundary conditions and stress boundary conditions being double integral,they unite into system of algebraic equations,then solve the unknown variables and get the solution of equation.This method can be combined with different boundary conditions uniting system of equations to solve the bending problem of moderately rectangular orthotropic thick plate under various boundaries conditions.The derivation and calculating of this method are simple,neat and unified.The bending problem is transformed into the solution of system of equations,with double cosine series system of equations and the unknown variables look very many and complicated,but very regular,and they are easy to computer programming.In order to verify the accuracy of the method,some mathematic examples,graphies and form gived in this paper are worked out by using MATLAB,it is easy to contrast and check.The bending theory of moderately rectangular orthotropic thick plate in this paper is simple,clear and easy to expand.Also it is helpful and practical for the development of plate theory and engineering application of highway,aviation,architecture and water conservancy.