A FINITE-ELEMENT APPROACH TO 3-DIMENSIONAL SINGULAR STRESS STATES IN ANISOTROPIC MULTIMATERIAL WEDGES AND JUNCTIONS

A finite element formulation is developed to determine the order and a ngular variation of singular stress states due to material and geometr ic discontinuities in anisotropic materials. The formulation applies t o any two-dimensional geometry that is prismatic in the third directio n and has three-dimensional displacement fields, In some special eases the three-dimensional fields become uncoupled antiplane and inplane f ields and this formulation yields the uncoupled results. The formulati on provides for the determination of the asymptotic stress and displac ement 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 ra dial direction measured from the singular point. The formulation of Ya mada and Okumura [(1983) Hybrid and Mixed Finite Element Methods, pp. 325-343. Wiley, Chichester] for inplane problems is adapted for this p urpose, The simplicity and accuracy of the formulation are demonstrate d by comparison with several analytical solutions for both isotropic a nd anisotropic multi-material wedges and junctions. The nature and spe ed of convergence associated with the element suggests that it could b e employed in developing two-dimensional and three-dimensional enriche d elements for use along with standard elements to yield accurate and computationally efficient solutions to problems having complex global geometries leading to singular stress states.