Numerical Analysis of Plane Elasticity Problems

The method is applicable to those two-dimensional elasticity problems having stress boundary conditions. The generalized presentation of results makes it possible to apply the method to many diversely shaped regions. The method results in a system of linear simultaneous equations. While the coefficient matrix of this set of equations is dense, it is well-conditioned and the unknowns can be determined with excellent accuracy using standard matrix procedures. The method is presented in a form easily adapted for digital computer solution. Excellent results are obtained in reasonable computing time. To demonstrate the accuracy and applicability of the method, the problem of stress concentration in long thin tensile members having semicircular notches is considered. Stress concentration factors are presented for radius-of-notch to minimum-member-width ratios ranging from 0.001 to 1.5. The results are in excellent agreement with previous analytical calculations and experimental data.