Intrinsic extended isogeometric analysis with emphasis on capturing high gradients or singularities. (English) Zbl 1521.74243
Summary: 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.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65D07 | Numerical computation using splines |
Keywords:
isogeometric analysis; extended finite-element method; partition of unity; sharp gradient; singularityReferences:
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