The idea of isogeometric analysis (IGA) is first proposed by Hughes, et al. [1], with an aim of bridging the existing gap between the worlds of finite element analysis (FEA) and computer-aided design (CAD). The root idea behind IGA is that the basis functions used to exactly model the geometry will also serve as the basis functions for the solution space of the numerical method. For the initial instantiation of IGA, non-uniform rational B-splines (NURBS) are chosen as the basis functions, due to their flexibility and precision.
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As the amount of related articles increases every year, IGA has drawn great attention and been put into practice rapidly by researchers. IGA is not restricted to NURBS, some other splines are also successfully employed in the analysis [14-20]. A series of new methods for IGA boundary problems are studied in Refs. [21-26]. Beam, shell and plate problems are hot fields where IGA has demonstrated its advantages [9, 18, 27-34]. In Refs. [35-44], IGA is perfected theoretically in efficiency, stability and accuracy. In the contest of model construction and optimization, IGA has shown advantages [23, 45-50]. Meanwhile, researchers work on the IGA domain treatment in Refs. [36, 5154]. IGA is not only employed in conventional mechanical applications, e.g., contact, fluids, vibration [55-60], but has also spread to the new, tough and complex fields [49, 61-63].
NURBS are obtained from B-splines, which are piecewise polynomial curves composed of linear combinations of B-spline basis functions. In this section, we give a brief review on B-splines and NURBS (See [2, 64]for more details ofB-splines andNURBS).
[15]D.C. Thomas, M.A. Scott, J.A. Evans, K. Tew, E.J. Evans, Bezier projection: A unified approach for local projection and quadrature-free refinement and coarsening of NURBS and T-splines with particular application to isogeometric design and analysis, Comput. Method. Appl. M. 284 (2015) 55-105.
[17]E.J. Evans, M.A. Scott, X. Li, D.C. Thomas, Hierarchical T-splines: Analysis-suitability, Bezier extraction, and application as an adaptive basis for isogeometric analysis, Comput. Method. Appl. M. 284 (2015) 1-20.
[60]H. Bayesteh, A. Afshar, S. Mohammdi, Thermo-mechanical fracture study of inhomogeneous cracked solids by the extended isogeometric analysis method, European Journal ofMechanics - A/Solids. 51 (2015) 123-139. 2ff7e9595c
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