NURBS-Enhanced Meshfree Method with an Integration Subtraction Technique for Complex Topology

Abstract

In this paper, we present an integration subtraction technique to model holes interactively in a predesigned domain for adaptive problems. This technique involves two approaches, the normal subtraction technique and the moving subtraction technique. In the basic normal subtraction technique, the predesigned domain can be meshed using any methods as an initial integration background cell for meshfree analysis. Holes are described using closed non-uniform rational B-spline (NURBS) curves to preserve the exact computer-aided design (CAD) geometry and are meshed alone using the homotopic method, so they can easily be subtracted from the predesigned domain with no refinement. On the other hand, when the hole size is varying, the moving subtraction technique, in which only the changing part between the new and old boundaries needs to be integrated and subtracted, is more efficient. Compared with the standard radial point interpolation method (RPIM) and finite element method (FEM) in three linear elastic examples with different holes, the excellent accuracy and good efficiency of the proposed method are demonstrated, and its feasibility in complex topology problems is verified.