Extended Isogeometric Analysis for Strong and Weak Discontinuities

Vinh Phu Nguyen, Stephane Pierre Alain Bordas

Research output: Chapter in Book/Report/Conference proceedingChapter (Book)Other

10 Citations (Scopus)

Abstract

Isogeometric analysis (IGA) is a fundamental step forward in computational mechanics that offers the possibility of integrating methods for analysis into Computer Aided Design (CAD) tools and vice versa. The benefits of such an approach are evident, since the time taken from design to analysis is greatly reduced leading to large savings in cost and time for industry. 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 Matlab® implementation, we present an introduction to IGA applied to the Finite Element (FE) method and 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 fracture examples in both two-dimensions and three-dimensions are given as illustration. The open source Matlab® code which accompanies the present paper can be applied to one, two and threedimensional 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. It also implements the Bézier extraction concept that allows FE analysis to be performed on T-spline geometries. An attempt was also made to include a review of recent developments of IGA.

Original languageEnglish
Title of host publicationIsogeometric Methods for Numerical Simulation
EditorsGernot Beer, Stephane Bordas
Place of PublicationVienna Austria
PublisherSpringer
Pages21-120
Number of pages100
Edition1
ISBN (Print)9783709118436
DOIs
Publication statusPublished - 1 Jan 2015
Externally publishedYes

Publication series

NameCISM International Centre for Mechanical Sciences, Courses and Lectures
Volume561
ISSN (Print)0254-1971
ISSN (Electronic)2309-3706

Keywords

  • Bernstein Polynomial
  • Control Point
  • Gauss Point
  • Isogeometric Analysis
  • Stress Intensity Factor

Cite this