Isogeometric analysis: An overview and computer implementation aspects

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, s...

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Bibliographic Details
Published inMathematics and computers in simulation Vol. 117; pp. 89 - 116
Main Authors Nguyen, Vinh Phu, Anitescu, Cosmin, Bordas, Stéphane P.A., Rabczuk, Timon
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.11.2015
Subjects
CAD
Finite elements
Isogeometric analysis
Isogeometric collocation
NURBS
Isogeometric analysis
Isogeometric collocation
Finite elements
CAD
NURBS
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Summary: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.
ISSN:0378-4754
1872-7166
DOI:10.1016/j.matcom.2015.05.008