NURBS-enhanced line integration boundary element method for 2D elasticity problems with body forces

A NURBS-enhanced boundary element method for 2D elasticity problems with body forces is proposed in this paper. The non-uniform rational B-spline (NURBS) basis functions are applied to construct the geometry and the model can be reproduced exactly at all stages since the refinement will not change the shape of the boundary. Both open curves and closed curves are considered. The fields are approximated by the traditional Lagrangian basis functions in parameter space, rather than by the same NURBS basis functions for geometry approximation. The parametric boundary elements and collocation nodes are defined from the knot vector of the curve and the refinement of the NURBS curve is easy. Boundary conditions can be imposed directly since the Lagrangian basis functions have the property of delta function. In addition, most methods for the treatment of singular integrals in traditional boundary element method can be applied in the proposed method. To overcome the difficulty for evaluation of the domain integrals in problems with body forces, a line integration method is further applied in this paper to compute the domain integrals without additional volume discretizations. Numerical examples have shown the accuracy of the proposed method.