  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. 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, implemen- tation 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. The open source Matlab 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 Bezier extraction concept that allows
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.
