Intrinsic extended isogeometric analysis with emphasis on capturing high gradients or singularities

• DOI: 10.1016/j.enganabound.2021.09.022
• Publication Date: 2021-10-22T02:19:53Z
• Authors: Xuan Peng; Haojie Lian; Zhenwu Ma; Chao Zheng
• Keywords: 0101 mathematics; 01 natural sciences

Abstract Formulations of an extra-degree-of-freedom (DOF) free extended isogeometric analysis (IGA) are presented in this study. The idea is achieved by reconstruction of the coefficients through a mesh-free-based local approximation, based on the framework of a generalized finite-element method. The enrichment functions are embedded in the mesh-free basis implicitly, resulting in an identical number of DOFs. Moreover, the system condition number is of the same level between the enriched IGA and non-enriched version. The approach to handling the blending issues is discussed. Numerical examples with a solution containing sharp features/singularities are designed and studied in terms of accuracy and convergence.