Isogeometric analysis: An overview and computer implementation aspects

By Vinh Phu Nguyen, Cosmin Anitescu, Stéphane P.A. Bordas, Timon Rabczuk. Mathematics and Computers in Simulation, 2012

723 citations recorded by the source corpus.

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 Bezier 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.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ba47d16970726fccc4acaceb6c24e3316aeb27a9

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Citations in the corpus

Deep Autoencoder based Energy Method for the Bending, Vibration, and Buckling Analysis of Kirchhoff Plates (2020, methodology): “…methods, a variety of numerical methods have been developed including the ﬁnite element method [2, 3], boundary element method [4, 5], meshfree method [6, 7], isogeometric analysis (IGA) formulations [8], numerical manifold method [9, 10, 11] and recently deep learning based methods [12, 13, 14].”
Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth (2017, methodology): “More details can be found in [84,60].”
An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications (2019, methodology): “Finally, the deep energy scheme is then compared with an open source IGA-FEM code from on this problem [37], which is also based on the kirchhoff plate theory.”
Implementation of regularized isogeometric boundary element methods for gradient‐based shape optimization in two‐dimensional linear elasticity (2016, methodology): “Isogeometric analysis A recent trend in shape optimization is IGA [46, 47], which integrates the geometry and analysis representations.”