Derivation of Annular Plate Sector Element for General Bending Analysis

Abstract

A new mathematical finite element model suitable for the general bending analysis of annular plate structure is developed in polar coordinates system depending on the strain based approach has been derived. The element is simple and contains only the essential degrees of freedom. The element has 15 degrees of freedom, three at each node and satisfies the exact representation of the rigid body modes of displacement. The results obtained by using the proposed element in several numerical problems have shown that a rapid convergence to exact solution can be obtained with acceptable degree of accuracy when only few element are used. The element has the advantage over the other available annular plate elements. The improvement obtained is due to the fact that all the displacement fields of the present element satisfy the exact representation of rigid body modes of displacements then the shape function error due to rigid body modes becomes zero. Also, the present element satisfies the full geometry of the annular plate due to this point discretization error becomes zero. Finally the error due to strain mode becomes very small because the present element satisfies the compatibility equations of strains and the 12th coefficients of strain mode derived exactly from partial differential equations of strains. The numerical solution of several problems by using the present element proved to be powerful in the structural bending analysis of circular annular plates. Its results are better than the solution of other elements and packages with respect to analytical.