Document Type

Thesis - Open Access

Award Date


Degree Name

Master of Science (MS)


Civil Engineering


The main objective for this investigation is to examine the applicability of the finite difference method in obtaining the elastic stress distribution in a square plate weakened by a large elliptical or circular notch. A square mesh is used with maximum subdivisions as allowed by the storage capacity of the computer available at South Dakota State University. The nodal points of the mesh are placed in such a way as to give an approximate outline of the circular or elliptical shape. The plates under study are simply supported along two edges and free along the other two, and subjected to uniform compression. Two types of notches are introduced at the center of the plate; one is circular and the other is elliptical in shape. With the aid of the electronic computer and the utilization of the finite difference technique principal stress contours in each plate are obtained. These stress contours for both the circular and the elliptical notches are compared. Such comparison will assist the structural designer in obtaining the more efficient type of notch. The stress distribution analysis consists of computing the following: (1) normal stresses acting in the x and y directions. (2) Shearing stress acting on the xy-plane. (3) Major and minor principal stresses and their orientations with respect to the x-axis. These quantities are computed at each nodal point through-out the section of plate. The finite difference computations are carried out with the aid of an electronic computer. The computer output for the stress distribution was printed out using a special board so that the results are shown on the actual plan shape of the plate section under consideration. This permitted stress contours to be drawn within the outline of the section. The solutions presented in this work provide a valuable source of information for future investigations. This analysis is of particular importance in the determination of buckling loads for plates identical to those investigated in this study.

Library of Congress Subject Headings

Strains and stresses




Number of Pages



South Dakota State University