ANALYSIS OF PLATE BENDING BY FINITE ELEMENT (DISPLACEMENT) METHOD

Abstract

A study of bending of plates for small deformations by applying the finite element method is presented in this thesis. This thesis is mainly concerned with the development of new displacement functions for rectangular and triangular elements. For reotangular elements, a method has been proposed for selecting displacement funotions in which trigonometric expression that had apparently failed to give satisfactory results in earlier attempts, can be used along with polynomial terms. The method leads to conforming displacement functions which satisfy the oonvergenoe criteria. Not many suitable conforming functions have been reported so far. But, the method developed here for rectangular elements shows how many more new displacement functions can be found, all of them satisfying the convergence oriteria. In fact, the number of such functions is almost unlimited. A conforming displacement function has been suggested for triangular elements by .using simple polynomial expressions. Continuity of normal slopes have been achieved by forcing them to vary linearly along the element boundaries. To accomplish this, additional correction functions have been used. Several plate bending problems have been solved using an IBM 1620 Model I computer. Results are presented for four different displacement functions; three are for rectangular elements and one for triangular elements. All the functions converge towards the true answers with successive refinements in the sub-division analysis. The convergence is mo no tonic in all Cases.