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Based on our proposed adaptivity strategy for the vibration of Reissner–Mindlin plate, we develop it to apply for the vibration of Kirchhoff plate. The adaptive algorithm is based on the Geometry-Independent Field approximaTion (GIFT), generalized from Iso-Geometric Analysis (IGA), and it can characterize the geometry of the structure with NURBS (Non-Uniform Rational B-Splines), and independently apply PHT-splines (Polynomial splines over Hierarchical T-meshes) to achieve local refinement in the solution field. The MAC (Modal Assurance Criterion) is improved to locate unique, as well as multiple, modal correspondence between different meshes, in order to deal with error estimation. Local adaptivity is carried out by sweeping modes from low to high frequency. Numerical examples show that a proper choice of the spline space in solution field (with GIFT) can deliver better accuracy than using NURBS solution field. In addition, for vibration of heterogeneous Kirchhoff plates, our proposed method indicates that the adaptive local  h -refinement achieves a better solution accuracy than the uniform  h -refinement.

Isogeometric Analysis with Local Adaptivity for Vibration of Kirchhoff Plate