Isogeometric analysis with local adaptivity based on a posteriori error estimation for elastodynamics

• Main Author: Yu, Peng
• Published: Cardiff University 2019
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.768107

IsoGeometric Analysis (IGA) was invented to integrate the Computer-Aided Design (CAD) and Computer-Aided Engineering (CAE) into a unified process. According to the recent research, IGA performs a super convergence in case of vibration, and especially, it perfectly addresses the Gibbs phenomenon (fluctuation) occurring in discrete spectra when using standard Finite Element Method (FEM). However, due to the tensor-product structure of Non-Uniform Rational B-Splines (NURBS), it fails to achieve the local refinement, which restricts its application to engineering fields performing local characteristics that require local refinement, such as sharp geometrical feature and/or varying material properties. In this context, the first goal of thesis is to extend the recently proposed paradigm, called Geometry Independent Field approximaTion (GIFT), to be applied in the scheme of dynamics. The GIFT methodology allows geometry of structure to be described within the NURBS provided directly by the existing CAD software, and solution field to be approximated by the Polynomial splines over Hierarchical Tmeshes (PHT) with the feature of local refinement meanwhile. Subsequently, in the framework of GIFT, an adaptivity technique based on hierarchical a posteriori error estimation on the modal vector is established for the free vibration of thick plate. The proposed adaptive mesh achieves a faster convergence than uniform refinement. Especially, the employment of Modal Assurance Criterion (MAC)-style strategy is able to better determine the modal correspondence between coarse and fine discretizations than Frequency Error Criterion (FEC) method. Furthermore, based on hierarchical a posteriori error estimation strategy, three types of adaptivity algorithms are constructed to deal with the space-time refinement. Specially, unidirectional multi-level space-time adaptive GIFT/Newmark (UM-STAGN) well catches stress wave propagation but fails in error information transfer. Energybased space-time adaptive GIFT/Newmark (E-STAGN) can reassess the error but cannot uncover the source of error. Dual weighted residual adaptive GIFT/Newmark (DWR-STAGN) methods are error-sensitive so that it leads to the best convergence among these three approaches.