A study of three numerical methods for the analysis of circular plates symmetrically bent
Austin, Walter J.
Master of Science
This dissertation contains a study of three numerical methods for the solution of radially symmetric plate bending problems. Two of the methods consist of numerical integration procedures applied to the well-known governing, differential equations. The first numerical integration technique proceeds one interval at a time and employs closed-type, consistent integration formulas based upon a linear variation of the highest derivatives in each interval. The second numerical technique proceeds two intervals at a time and employs closed-type, consistent integration formulas based upon a parabolic variation of the highest derivatives in the two intervals. In both methods recurrence formulas are used to avoid iteration. The third numerical method is an original finite element procedure which employs finite difference expressions to evaluate the bending moments. The accuracies of the three methods have been investigated by applying them to ten problems of wide diversity, including plates with and without a central hole, with uniform and with non-uniform thickness, and with abrupt steps in the thickness, and subjected to edge couples and shears, distributed loadings, ring line loads, and with concentrated load at the center. The outer edge is considered to be either fixed or hinged in all problems. The numerical solutions of the ten problems by the three methods are presented herein in complete form. In a number of the problems solutions have been obtained for several interval sizes. These solutions are compared with each other and with the exact solutions to give an indication of the accuracies of the methods.