NE-IIBEFM for problems with body forces: A seamless integration of the boundary type meshfree method and the NURBS boundary in CAD

A NURBS-enhanced interpolating boundary element-free method (NE-IIBEFM) is proposed by coupling the meshfree method with the non-uniform rational B-spline (NURBS). The NURBS plays an essential role in computer aided design (CAD) whereby it can be used as the bridge between boundary type meshless method and CAD, which is convenient and is widely utilized in engineering. The NURBS basis functions used in CAD packages for geometry construction are applied to describe the boundary in the numerical procedure. Thus, the geometry of the curve can be reproduced exactly at all stages. The boundary integral cells and nodes are defined from the knot vector in NURBS, and both the open and closed curves are considered. The fields are approximated by an improved interpolating moving least square method, in which the obtained shape functions have the property of delta function. Thus, the boundary conditions can be imposed directly. A line integration method without domain discretization is further coupled with the proposed method for the treatment of domain integrals for problems with body forces.