Determination of Stress Concentration Factors in Flat Plates with Holes Using Finite-Element Analysis Methods

Abstract

The importance of stress concentration factors in machines and stuctures led to the development of various experimental and analytical techniques for determining them. One of these methods is the application of finite element analysis to the various structures. A common structural element in a piece of machinery is a flat plate with one or more bolt holes, that are often off center. Using certain assumptions from S. P. Timoshenko's Strength of Materials and the finite element method outlined in J. S. Przemienieck's, Theory of Matrix Stuctural Analysis, a computer program was written to help determine these stress concentration factors. The program consists of a main program that generates the nodal points, several subroutines that develop the stiffness matrix, a subroutine that transforms tIle element stiffness matrix into a system stiffness matrix, a subroutine that inverts a part of the system matrix, and a subroutine that multiplies the system deformations by another portion of the stiffness matrix. The stresses computed with the system do not correlate with other theoretical values. This inconsistency is believed to be caused by an error in the transformation of the element stiffness matrices into the system stiffness matrix. When this problem is adjusted, the program should give valid stress concentrations.