An improved isogeometric boundary element method approach in two dimensional elastostatics

The NURBS based isogeometric analysis offers a novel integration between the CAD and the numerical structural analysis codes due to its superior capacity to describe accurately any complex geometry. Since it was proposed in 2005, the approach has attracted rapidly growing research interests and wide applications in the Finite Element context. Only recently, in 2012, it was successfully tested together with the Boundary Element Method. The combination of the isogeometric approach and the Boundary Element Method is efficient since both the NURBS geometrical representation and the Boundary Element Method deal with quantities entirely on the boundary of the problem. Actually, there are still some difficulties in imposing generic boundary conditions, mainly due to the fact that the NURBS basis functions are not interpolatory functions. In this work it is shown that the direct imposition of the inhomogeneous generic boundary conditions to the NURBS control points may lead to significant errors. Consequently an improved formulation is proposed that relates the boundary conditions to the governing unknown variables by developing a transformation strategy. Several elasticity problems evince that higher solution accuracy can be achieved by the present formulation.