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Isogeometric analysis: an overview and computer implementation aspects
Nguyen, Vinh-Phu; Anitescu, Cosmin; Bordas, Stéphane et al.
2013
 

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Keywords :
isogeometric analysis, linear elasticity, Matlab⃝R , NURBS, finite elements, partition of unity, enrichment, 3D cracks, boundary conditions, CAD, large displacements and rotations, shells; IGA; Implementation; MATLAB; Code; tutorial; primer
Abstract :
[en] 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. The tight coupling of CAD and analysis within IGA requires knowledge from both fields and it is one of the goals of the present paper to outline much of the commonly used notation. In this manuscript, through a clear and simple Matlab⃝R implementation, we present an introduction to IGA applied to the Finite Element (FE) method and related computer implementation aspects. Furthermore, implemen- tation 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. The open source Matlab⃝R 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 B ́ezier extraction concept that allows 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.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Nguyen, Vinh-Phu
Anitescu, Cosmin
Bordas, Stéphane ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
Rabczuk, Timon
Language :
English
Title :
Isogeometric analysis: an overview and computer implementation aspects
Publication date :
August 2013
Collection name :
Legato Lab Report
Institution :
Unilu - University of Luxembourg, Luxembourg
Focus Area :
Computational Sciences
European Projects :
FP7 - 289361 - INSIST - Integrating Numerical Simulation and Geometric Design Technology
Funders :
CE - Commission Européenne [BE]
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since 06 January 2014

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