TY - JOUR
T1 - Isogeometric analysis
T2 - An overview and computer implementation aspects
AU - Nguyen, Vinh Phu
AU - Anitescu, Cosmin
AU - Bordas, Stéphane P.A.
AU - Rabczuk, Timon
N1 - Funding Information:
The authors would like to acknowledge the partial financial support of the Framework Programme 7 Initial Training Network Funding under grant number 289361 “Integrating Numerical Simulation and Geometric Design Technology”. Stéphane Bordas also thanks partial funding for his time provided by (1) the EPSRC under grant EP/G042705/1 Increased Reliability for Industrially Relevant Automatic Crack Growth Simulation with the eXtended Finite Element Method and (2) the European Research Council Starting Independent Research Grant (ERC Stg Grant Agreement No. 279578 ) entitled “Towards real time multiscale simulation of cutting in non-linear materials with applications to surgical simulation and computer guided surgery”. The first author would like to express his gratitude towards Professor L.J. Sluys at Delft University of Technology, The Netherlands for his support during the Ph.D. period and the Framework Programme 7 Initial Training Network Funding. The authors acknowledge Dr. Robert Simpson whose comments have improved the paper.
Publisher Copyright:
© 2015 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
PY - 2015/3/1
Y1 - 2015/3/1
N2 - 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.
AB - 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.
KW - CAD
KW - Finite elements
KW - Isogeometric analysis
KW - Isogeometric collocation
KW - NURBS
UR - http://www.scopus.com/inward/record.url?scp=84938421837&partnerID=8YFLogxK
U2 - 10.1016/j.matcom.2015.05.008
DO - 10.1016/j.matcom.2015.05.008
M3 - Article
AN - SCOPUS:84938421837
VL - 117
SP - 89
EP - 116
JO - Mathematics and Computers in Simulation
JF - Mathematics and Computers in Simulation
SN - 0378-4754
M1 - 4190
ER -