Spline-based meshfree method

In the present work, the spline-based meshfree method (SBMFM) is presented. The SBMFM uses spline basis functions for field variables and boundary representation. Because of the inherent properties of splines, that is, NURBS (nonuniform rational B-splines), the analysis domain used in the SBMFM has its own parametric domain. Unlike the classical concepts in the Computer-aided design (CAD) community in which the NURBS patches are used to model the body, the NURBS patch is treated as a background mesh in the present work. The real analysis domain is created by trimming operation so that the domain boundaries are described by spline curves only on a single NURBS patch. Building the geometry in this way enables a convenient boundary representation of the domains because direct manipulation of spline curves becomes possible. From a deformation point of view, the mesh distortion problem is effectively avoided even if the analysis domain undergoes a large deformation. In the SBMFM, boundary spline curves freely move with complete independence from the quadrilateral background NURBS patch. The so-called element connectivity is unnecessary for geometry description. In this paper, geometrically nonlinear problems are considered. Implementation strategy is presented and the effectiveness of the present SBMFM is shown through various numerical examples. Copyright (C) 2012 John Wiley & Sons, Ltd.