A finite element approach to three-dimensional singular stress states in anisotropic multi-material wedges and junctions

finite element formulation is developed to determine the order and angular variation of singular stress states due to material and geometric discontinuities in anisotropic materials. The formulation applies to any two-dimensional geometry that is prismatic in the third direction and has three-dimensional displacement fields. In some special cases the three-dimensional fields become uncoupled antiplane and inplane fields and this formulation yields the uncoupled results. The formulation provides for the determination of the asymptotic stress and displacement fields present at interior singular points of three-dimensional structures. The displacement field of the sectorial finite element is quadratic in the angular coordinate direction and asymptotic in the radial direction measured from the singular point. The formulation of Yamada and Okumura [(1983) Hybrid and Mixed Finite Element Methodr, pp. 325-343. Wiley, Chichester] for inplane problems is adapted for this purpose. The simplicity and accuracy of the formulation are demonstrated by comparison with several analytical solutions for both isotropic and anisotropic multi-material wedges and junctions. The nature and speed of convergence associated with the element suggests that it could be employed in developing two-dimensional and three-dimensional enriched elements for use along with standard elements to yteld accurate and computationally efficient solutions to problems having complex global geometries leading to singular stress states.