Robustness of isogeometric structural discretizations under severe mesh distortion

This paper investigates higher-order and higher-continuity functions in isogeometric structural analysis under distortion of the control and physical meshes. First, the concepts behind isogeometric analysis are briefly reviewed. The effect of perturbing control points upon the geometrical mapping is observed in the one-dimensional setting. The concept is extended to multiple dimensions with a series of cases where the interior of a cube is distorted in different ways and patch tests are performed to assess accuracy. A circular fillet patch is introduced through the appropriate degeneration of a control mesh in order to address the problem of modeling small features in finite element models. The fillet patch is tested with two problems of linear elasticity and is shown to be accurate. The investigation is further extended to the setting of large-deformation nearly incompressible nonlinear elasticity with two examples which make use of the recently proposed F¯ projection method.