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Isogeometric analysis: An overview and computer implementation aspects

Author

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  • Nguyen, Vinh Phu
  • Anitescu, Cosmin
  • Bordas, Stéphane P.A.
  • Rabczuk, Timon

Abstract

Isogeometric analysis (IGA) represents a recently developed technology in computational mechanics that offers the possibility of integrating methods for analysis and Computer Aided Design (CAD) into a single, unified process. The implications to practical engineering design scenarios are profound, since the time taken from design to analysis is greatly reduced, leading to dramatic gains in efficiency. In this manuscript, through a self-contained Matlab® implementation, we present an introduction to IGA applied to simple analysis problems and the related computer implementation aspects. Furthermore, implementation of the extended IGA which incorporates enrichment functions through the partition of unity method (PUM) is also presented, where several examples for both two-dimensional and three-dimensional fracture are illustrated. We also describe the use of IGA in the context of strong-form (collocation) formulations, which has been an area of research interest due to the potential for significant efficiency gains offered by these methods. The code which accompanies the present paper can be applied to one, two and three-dimensional problems for linear elasticity, linear elastic fracture mechanics, structural mechanics (beams/plates/shells including large displacements and rotations) and Poisson problems with or without enrichment. The Bézier extraction concept that allows the FE analysis to be performed efficiently on T-spline geometries is also incorporated. The article includes a summary of recent trends and developments within the field of IGA.

Suggested Citation

  • Nguyen, Vinh Phu & Anitescu, Cosmin & Bordas, Stéphane P.A. & Rabczuk, Timon, 2015. "Isogeometric analysis: An overview and computer implementation aspects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 117(C), pages 89-116.
    • Handle: RePEc:eee:matcom:v:117:y:2015:i:c:p:89-116
    DOI: 10.1016/j.matcom.2015.05.008
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    References listed on IDEAS

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    1. Nguyen, Vinh Phu & Rabczuk, Timon & Bordas, Stéphane & Duflot, Marc, 2008. "Meshless methods: A review and computer implementation aspects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 763-813.
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    Cited by:

    1. Xiaoying Zhuang & Binh Huy Nguyen & Subbiah Srivilliputtur Nanthakumar & Thai Quoc Tran & Naif Alajlan & Timon Rabczuk, 2020. "Computational Modeling of Flexoelectricity—A Review," Energies, MDPI, vol. 13(6), pages 1-29, March.
    2. Theodosiou, T.C., 2021. "Derivative-orthogonal non-uniform B-Spline wavelets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 368-388.
    3. Jingwen Ren & Hongwei Lin, 2023. "A Survey on Isogeometric Collocation Methods with Applications," Mathematics, MDPI, vol. 11(2), pages 1-21, January.
    4. Bo He & Brahmanandam Javvaji & Xiaoying Zhuang, 2019. "Characterizing Flexoelectricity in Composite Material Using the Element-Free Galerkin Method," Energies, MDPI, vol. 12(2), pages 1-18, January.
    5. Tan N. Nguyen & L. Minh Dang & Jaehong Lee & Pho Van Nguyen, 2022. "Load-Carrying Capacity of Ultra-Thin Shells with and without CNTs Reinforcement," Mathematics, MDPI, vol. 10(9), pages 1-25, April.
    6. Khadija Yakoubi & Ahmed Elkhalfi & Hassane Moustabchir & Abdeslam El Akkad & Maria Luminita Scutaru & Sorin Vlase, 2023. "An Isogeometric Over-Deterministic Method (IG-ODM) to Determine Elastic Stress Intensity Factor (SIF) and T-Stress," Mathematics, MDPI, vol. 11(20), pages 1-12, October.
    7. Yanming Xu & Haozhi Li & Leilei Chen & Juan Zhao & Xin Zhang, 2022. "Monte Carlo Based Isogeometric Stochastic Finite Element Method for Uncertainty Quantization in Vibration Analysis of Piezoelectric Materials," Mathematics, MDPI, vol. 10(11), pages 1-17, May.
    8. Yi Qiu & Cheng Xu & Jiangpeng Peng & Yanjie Song, 2024. "Isogeometric Topology Optimization of Multi-Material Structures under Thermal-Mechanical Loadings Using Neural Networks," Mathematics, MDPI, vol. 12(15), pages 1-21, July.
    9. Soufiane Montassir & Hassane Moustabchir & Ahmed Elkhalfi & Maria Luminita Scutaru & Sorin Vlase, 2021. "Fracture Modelling of a Cracked Pressurized Cylindrical Structure by Using Extended Iso-Geometric Analysis (X-IGA)," Mathematics, MDPI, vol. 9(23), pages 1-22, November.
    10. Yassopoulos, Christopher & Reddy, J.N. & Mortari, Daniele, 2023. "Analysis of nonlinear Timoshenko–Ehrenfest beam problems with von Kármán nonlinearity using the Theory of Functional Connections," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 709-744.

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