A two-dimensional Isogeometric Boundary Element Method for elastostatic analysis

The concept of isogeometric analysis, where functions that are used to describe geometry in CAD software are used to approximate the unknown fields in numerical simulations, has received great attention in recent years. The method has the potential to have profound impact on engineering design, since the task of meshing, which in some cases can add significant overhead, has been circumvented. Much of the research effort has been focused on finite element implementations of the isogeometric concept, but at present, little has been seen on the application to the Boundary Element Method. The current paper proposes an Isogeometric Boundary Element Method (BEM), which we term IGABEM, applied to two-dimensional elastostatic problems using Non-Uniform Rational B-Splines (NURBS). We find it is a natural fit with the isogeometric concept since both the NURBS approximation and BEM deal with quantities entirely on the boundary. The method is verified against analytical solutions where it is seen that superior accuracies are achieved over a conventional quadratic isoparametric BEM implementation.

► A 2D Isogeometric Boundary Element Method is introduced for the first time.
► NURBS functions are used to approximate geometry, displacement and traction fields.
► Collocation is used to for a system of equations at the Greville abscissae.
► The method is verified against closed-form solutions.
► Comparison is made with the Finite Element Method.