Multi-material Wedges Research Articles

Finite element analysis of anisotropic materials with singular inplane stress fields

A finite element formulation is developed for the analysis of singular stress states at material and geometric discontinuities in anisotropic materials loaded inplane. The displacement field of the sectorial element is quadratic in the angular coordinate direction and exponential in the radial direction measured from the singular point. The formulation of Yamada and Okumura (1983a, b) is extended to take into account the anisotropy of the material. The stress and displacement fields are obtained when the order of the stress singularity is real as well as complex. When the order of the stress singularity is complex, it is shown that the angular variation of the stress and displacement fields can be expressed in an infinite number of ways. Results for the displacement and stress fields obtained when the order of the stress singularity is complex can be made to match already published results once a similarity transformation is applied. The simplicity and accuracy of the formulation are demonstrated by comparison to several analytical solutions for both isotropic and anisotropic multi-material wedges and junctions with and without disbonds. The nature and rate of convergence associated with the element suggests that it could be used in developing enriched elements for use with standard elements to yield accurate and computationally efficient solutions to problems having complex global geometries.