Examination of a Semi-Analytic Finite Element for Plate Bending Problems

Abstract

In this thesis the Semi-Analytic Finite Element Method of analysis of laterally loaded rectangular plates is examined. A computer program is described in which the eigenfunctions of free vibration of uniform beams are used as the analytic functions. Rectangular plates with any combination of simply supported, clamped or free edges and with any variation of loading or flexural rigidity, including plates with holes or rigid inclusions, may be solved. In developing the computer program, various schemes were implemented to reduce the influence of errors inherent in the beam eigenfunctions and for the reduction of computer storage requirement so that it may, be possible to process the program on a relatively small digital computer. A description of these schemes is given in this thesis. Using the computer program, the behaviour of the analytic functions in respect of numerical stability and convergence is examined on a comparative basis and the effects of load and rigidity variation on these characteristics are established. Extensive tests are carried out to check the accuracy of the method under various conditions of loading and rigidity variations. Also, the rate of convergence of the semi analytic method is compared with other finite element formulations. Finally, the results from the semi-analytic method, for three plate problems, are compared with those from an experimental technique, namely the Moire method.