TY - CHAP
T1 - Extended Isogeometric Analysis for Strong and Weak Discontinuities
AU - Nguyen, Vinh Phu
AU - Bordas, Stephane Pierre Alain
PY - 2015/1/1
Y1 - 2015/1/1
N2 - 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.
AB - 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.
KW - Bernstein Polynomial
KW - Control Point
KW - Gauss Point
KW - Isogeometric Analysis
KW - Stress Intensity Factor
UR - http://www.scopus.com/inward/record.url?scp=85051977967&partnerID=8YFLogxK
U2 - 10.1007/978-3-7091-1843-6_2
DO - 10.1007/978-3-7091-1843-6_2
M3 - Chapter (Book)
SN - 9783709118436
T3 - CISM International Centre for Mechanical Sciences, Courses and Lectures
SP - 21
EP - 120
BT - Isogeometric Methods for Numerical Simulation
A2 - Beer, Gernot
A2 - Bordas, Stephane
PB - Springer
CY - Vienna Austria
ER -