Any In-plane Loads Circular Plate Bending, Vibration And Buckling Analysis

This paper uses Ritz theory and presents a method to solve the problem of bend, free vibration and buckling properties of the circular plates subjected to arbitrary forces. Firstly, the expressions of the in-plane stress of circular plates that is subjected to a pair of concentrated forces in polar coordinates are derived and the in-plane stress equations are obtained subjected to many pairs of concentrated forces and arbitrary forces. Secondly, the general matrix equations of bend, free vibration and buckling are obtained by the means of method of Ritz method. Then, this paper use Fortran to obtain solution of bend, free vibration and buckling of a circular plates. Finally, the roots of the bend, buckling, frequency of the equation can be numerically worked out. The method can give the results with high precision. The calculating cost is little, the course of the analysis is rather simple and the programming is easy.The paper takes simply supported circular as example. The numerical results demonstrate the convergence and accuracy of the present method.