A family of elements with λ singularity

A new finite element family which contains a λ singularity is developed. Three elements are derived; namely three-, four- and five-noded elements which are compatible with linear, quadratic and cubic standard isoparametric finite elements, respectively. The elements are tested on two different examples. In the first example, an edge crack problem is analysed 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 λ. The results of those examples illustrate the efficiency of the proposed elements.