Isogeometric analysis: An overview and computer implementation aspects

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

Research output: Contribution to journalArticle

251 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number4190
Pages (from-to)89-116
Number of pages28
JournalMathematics and Computers in Simulation
Volume117
DOIs
Publication statusPublished - 2015 Mar 1

Keywords

  • CAD
  • Finite elements
  • Isogeometric analysis
  • Isogeometric collocation
  • NURBS

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)
  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

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