Accuracy of several finite difference methods for plate problems
Doshi, Arvind D
Austin, Walter J.
Master of Science
The accuracy of several finite difference methods for the analysis of the flexure of plates with fixed edges is studied in this dissertation. The investigation has been confined to a study of a square fixed edge plate subjected to uniform loading. Three different approaches are taken. First, the accuracy of the solutions obtained by the conventional finite difference procedure on a uniform square network was investigated by solving the test problem with seven different sizes of networks. Then the improvement of the accuracy of these solutions by the Richardson's extrapolation technique was studied. The second approach involved the use of graded networks with finer divisions near the fixed edge. Two different network patterns were used. The improvement of accuracy with the increase in fineness of the net was determined. The Richardson's extrapolation procedure was also studied to examine if it is useful for graded networks. Finally, in the third approach the use of higher order differences was investigated for uniform networks. A comparison is made of the accuracy of the various methods discussed above.