Improved method for determining free boundary stresses

Abstract

The conventional finite element method shows its weakness in determining the stress distributions along free boundaries. This is because the chosen element displacement functions do not implicitly satisfy the conditions which prevail at the free boundaries. A procedure has been proposed to modify the conventional finite element method so as to allow the elastic stresses along the free boundaries of two- and three-dimensional structures to be determined with improved accuracy. The results obtained by this modified method for a two-dimensional problem are compared with both a photoelastic and a traditional finite element solution. The comparison shows that the modified solution is in better agreement with the photoelastic test data as compared with the traditional solution. The results obtained by the modified method for a three-dimensional problem is compared with a traditional finite element solution and the former is found to be superior.