CLASSICAL SOLUTION SHAPE FUNCTIONS IN THE FINITE ELEMENT ANALYSIS OF CIRCULAR AND ANNULAR PLATES

The objective of this work is to present a new method for the dynamic and static analysis of thin, elastic, isotropic, non-uniform circular and annular plates. The method is a combination of plate theory and Þnite element analysis. The plate is divided into one circular and many annular Þnite elements. The displacement functions are derived from SandersÕ classical plate theory. These displacement functions satisfy the convergence criteria of the Þnite element method. The matrices for mass and sti¤ness are determined by precise analytical integration. A computer programme has been developed, the convergence criteria have been established, and the natural frequencies and vibration modes have been computed for di¤erent cases. The results obtained reveal that the frequencies calculated by this method are in good agreement with those obtained by other authors.