Study on the local refinement in spline finite element method by using hierarchical B-spline

Abstract

A new local refinement scheme for spline finite element method has been proposed; this scheme involves the use of hierarchical B-spline. NURBS has been widely used in CAD; however, the local refinement of NURBS is difficult due to its tensor-product property. In this study, we attempted to use hierarchical B-splines as local refinement strategy in spline FEM. The regions of high gradients are overlapped by hierarchically-created local meshes. Knot vectors and control points in local meshes are extracted from global meshes, and they are refined using specific schemes. Proper compatibility conditions are imposed between global and local meshes. The effectiveness of the proposed method is verified on the basis of numerical results. Further, it is shown that by using a proposed local refinement scheme, the accuracy of the solution can be improved and it could be higher than that of the solution of a conventional spline FEM with relatively lower degrees of freedom. © 2010 The Korean Society of Mechanical Engineers.