Stress analysis around holes or notches by special finite elements

In this paper, three special elements for stress concentration analysis around holes or notches are presented. One is based on a variational principle involving displacements, unsymmetric stresses and rotations as independent variables, the other two on the classical Hellinger-Reissner principle. The new elements are designed to be used in a single layer along the cavity rim, where enhanced properties are needed to get a satisfactory level of accuracy. Special properties are obtained by enforcing the stress approximation to satisfy a priori the traction-free boundary condition on the element side positioned along the cavity rim and by properly enriching the displacement interpolation. The proposed elements are: applicable to geometries of arbitrary shape, easy-to-use, low-cost and readily implementable into existing finite element codes.