Isogeometric Analysis with Hierarchical B-Splines for Planar Structural Dynamics with Large Deformation

In order to develop the adaptive mesh refinement algorithm for planar structural dynamics with large deformation, the construction of hierarchical B-spline basis functions for isogeometric analysis and the multi-level Bézier extraction approach restudied. In order to maintain the uniformity of element basis functions, the multi-level Bézier extraction approach was employed to present a standard element structure for the hierarchical B-spline during analysis process. Furthermore, the super-convergence patch recovery method was applied to obtain the reference stress in the adaptive analysis. Therefore, the refinement domain determined based on the energy norm error, which calculated via the reference stress and the numerical stress during the error estimation. Finally, the effectiveness and accuracy of the isogeometric analysis based on the hierarchical B-spline are validated by a static example of an elastic plate with circular hole and a planar structural dynamic example with large deformation.