A 2-D four-noded finite element containing a singularity of order λ

A 2-D four-noded finite element which contains a <TEX>${\lambda}$</TEX> singularity is developed. The new element is compatible with quadratic standard isoparametric elements. The element is tested on two different examples. In the first example, an edge crack problem is analyzed using two different meshes and different integration orders. The second example is a crack perpendicular to the interface problem which is solved for different material properties and in turn different singularity order <TEX>${\lambda}$</TEX>. The results of those examples illustrate the efficiency of the proposed element.