NURBS

A NURBS enhanced extended finite element approach for unfitted CAD analysis. A NURBS enhanced extended finite element approach is proposed for the unfitted simulation of structures defined by means of CAD parametric surfaces. In contrast to classical X-FEM that uses levelsets to define the geometry of the computational domain, exact CAD description is considered here. Following the ideas developed in the context of the NURBS-enhanced finite element method, NURBS-enhanced subelements are defined to take into account the exact geometry of the interface inside an element. In addition, a high-order approximation is considered to allow for large elements compared to the size of the geometrical details (without loss of accuracy). Finally, a geometrically implicit/explicit approach is proposed for efficiency purpose in the context of fracture mechanics. In this paper, only 2D examples are considered: It is shown that optimal rates of convergence are obtained without the need to consider shape functions defined in the physical space. Moreover, thanks to the flexibility given by the Partition of Unity, it is possible to recover optimal convergence rates in the case of re-entrant corners, cracks and embedded material interfaces.


References in zbMATH (referenced in 27 articles , 1 standard article )

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  1. Jiang, Wen; Liu, Yingjie; Annavarapu, Chandrasekhar: A weighted Nitsche’s method for interface problems with higher-order simplex elements (2022)
  2. Tong, Yan; Müller, Michael; Ostermeyer, Georg-Peter: A mortar-based cavitation formulation using NURBS-based isogeometric analysis (2022)
  3. Wu, Chunlin; Zhang, Liangliang; Song, Gan; Yin, Huiming: Inclusion-based boundary element method for virtual experiments of particulate composites containing arbitrarily shaped inhomogeneities (2022)
  4. Legrain, Grégory: Non-negative moment fitting quadrature rules for fictitious domain methods (2021)
  5. Audoux, Yohann; Montemurro, Marco; Pailhès, Jérôme: Non-uniform rational basis spline hyper-surfaces for metamodelling (2020)
  6. Gervasio, Paola; Dedè, Luca; Chanon, Ondine; Quarteroni, Alfio: A computational comparison between isogeometric analysis and spectral element methods: accuracy and spectral properties (2020)
  7. Sevilla, Ruben; Zlotnik, Sergio; Huerta, Antonio: Solution of geometrically parametrised problems within a CAD environment via model order reduction (2020)
  8. Zang, Quansheng; Liu, Jun; Ye, Wenbin; Lin, Gao: Isogeometric boundary element for analyzing steady-state heat conduction problems under spatially varying conductivity and internal heat source (2020)
  9. Codony, D.; Marco, O.; Fernández-Méndez, S.; Arias, I.: An immersed boundary hierarchical B-spline method for flexoelectricity (2019)
  10. Hirschler, T.; Bouclier, R.; Duval, A.; Elguedj, T.; Morlier, J.: The embedded isogeometric Kirchhoff-Love shell: from design to shape optimization of non-conforming stiffened multipatch structures (2019)
  11. Pan, Qing; Rabczuk, Timon; Xu, Gang; Chen, Chong: Isogeometric analysis for surface PDEs with extended Loop subdivision (2019)
  12. Bouclier, Robin; Passieux, Jean-Charles: A Nitsche-based non-intrusive coupling strategy for global/local isogeometric structural analysis (2018)
  13. Coelho, Marianna; Roehl, Deane; Bletzinger, Kai-Uwe: Material model based on NURBS response surfaces (2017)
  14. Qin, X. C.; Dong, C. Y.; Wang, F.; Qu, X. Y.: Static and dynamic analyses of isogeometric curvilinearly stiffened plates (2017)
  15. Van Do, Vuong Nguyen; Ong, Thanh Hai; Thai, Chien H.: Dynamic responses of Euler-Bernoulli beam subjected to moving vehicles using isogeometric approach (2017)
  16. Zhou, Wei; Liu, Biao; Wang, Qiao; Cheng, Yonggang; Ma, Gang; Chang, Xiaolin; Chen, Xudong: NURBS-enhanced boundary element method based on independent geometry and field approximation for 2D potential problems (2017)
  17. Kudela, László; Zander, Nils; Kollmannsberger, Stefan; Rank, Ernst: Smart octrees: accurately integrating discontinuous functions in 3D (2016)
  18. Safdari, Masoud; Najafi, Ahmad R.; Sottos, Nancy R.; Geubelle, Philippe H.: A NURBS-based generalized finite element scheme for 3D simulation of heterogeneous materials (2016)
  19. Stavrev, Atanas; Nguyen, Lam H.; Shen, Ruyi; Varduhn, Vasco; Behr, Marek; Elgeti, Stefanie; Schillinger, Dominik: Geometrically accurate, efficient, and flexible quadrature techniques for the tetrahedral finite cell method (2016)
  20. Bayesteh, H.; Afshar, A.; Mohammdi, S.: Thermo-mechanical fracture study of inhomogeneous cracked solids by the extended isogeometric analysis method (2015)

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