Adaptive isogeometric analysis based on a combined r-h strategy

Abstract

ABSTRACTIn the present work, an r-h adaptive isogeometric analysis is proposed for plane elasticity problems. For performing the r-adaption, the control net is considered to be a network of springs with the individual spring stiffness values being proportional to the error estimated at the control points. While preserving the boundary control points, relocation of only the interior control points is made by adopting a successive relaxation approach to achieve the equilibrium of spring system. To suit the noninterpolatory nature of the isogeometric approximation, a new point-wise error estimate for the h-refinement is proposed. To evaluate the point-wise error, hierarchical B-spline functions in Sobolev spaces are considered. The proposed adaptive h-refinement strategy is based on using De-Casteljau’s algorithm for obtaining the new control points. The subsequent control meshes are thus obtained by using a recursive subdivision of reference control mesh. Such a strategy ensures that the control points lie in the physical domain in subsequent refinements, thus making the physical mesh to exactly interpolate the control mesh and thereby allowing the exact imposition of essential boundary conditions in the classical isogeometric analysis (IGA). The combined r-h adaptive refinement strategy results in better convergence characteristics with reduced errors than r- or h-refinement. Several numerical examples are presented to illustrate the efficiency of the proposed approach.