Enrichment functions for weak singularities in 2D elastic problems with isotropic and orthotropic materials

In this paper a new enrichment technique is presented for weak singularities in isotropic and orthotropic 2D linear elasticity problems. With absolutely no information of the singularity order, in a novel numerical approach, the enriching bases are constructed through a weighted residual imposition of the partial differential equation. Conceptually, the bases can be categorized as equilibrated basis functions. As another advantage of the proposed technique, it will be shown that the enriched solution may be extracted for either isotropic or orthotropic materials in a similar manner, noting that singularity effect in orthotropic materials has not been as widely referred to as for isotropic materials in the literature. The presented examples selected from the well-known literature reveal the accuracy and applicability of the enrichment in the framework of a boundary type method. The method may also be found useful for the researchers focusing on the eXtended Finite Element Method or other similar mesh-based or mesh-less methods.