On the configurational-force-based r-adaptive mesh refinement in isogeometric analysis

This paper discusses the main concept of the theory of configurational force based r-adaptive mesh refinement, in the context of isogeometric analysis (IGA). The investigation is restricted to linear elasticity and small displacements are assumed. The configurational forces are used for the quantification of numerical errors of the solution. Minimizing their values, the optimal discretization parameters can be determined. Since the configurational forces can be computed both on the control points and on the knots, with the application of this method, three different approaches are considered. At first, r-adaptive method is used to perform the control polygon refinement that is similar to the original idea proposed by Braun (1997) [3]. Additionally, with slight modification of the first method, knot-vector refinement can also be carried out. The simultaneous application of the two strategy is straightforward. The implemented methods are tested on two plane problems and the results are compared to the analytical solution.