Partition of unity and drilling rotations in the boundary element method (BEM)

This paper presents a novel approach to include drilling rotations in the classical two-dimensional boundary element method. The approach is based on a simple partition of unity strategy that gives rise to a fictitious rotational degree of freedom (using the well known Allman’s triangle strategy). A functional based on the rotational residual ties the average fictitious drilling rotation field to the true rotation field induced from the two-dimensional elasticity problem and additionally provides the required extra equation for the enriched BEM formulation. The approach maintains the boundary only character of BEM and the partition of unity enrichment makes it general (totally kernel independent) and efficient (just certain areas of the boundary could be enriched). The accuracy of the proposed method is assessed with well known benchmark problems (e.g. Cook’s membrane).