V. Calo1, R. de Borst2, T.J.R. Hughes3, T. Kvamsdal4, A. Reali5, G. Sangalli5, C.V. Verhoosel2
1KAUST/SA, 2Eindhoven University of Technology/NL, 3University of Texas at Austin/US, 4SINTEF Information and Communication Technology, Norway/NO, 5University Pavia/IT
In recent years isogeometric analysis (IGA) has become a viable tool for solving many problems of scientific and engineering interest. Fields of application include thin-walled structures, fluid-structure interactions, failure mechanics, biomedical engineering, and others. Current research on isogeometric analysis is driven by two main motivations. First, isogeometric analysis avoids cumbersome geometry clean-up and meshing operations by directly using the geometric model for analysis. Avoiding meshing operations has been shown to particularly pay off for complex (engineering) structures. A second advantage of isogeometric analysis is that the spline bases underlying the analyses have attractive properties compared to traditional finite elements. The ability to control inter-element continuity conditions and to perform local refinements (using e.g. T-splines) are just two of those advantageous properties.
The excellent results obtained using isogeometric analysis have been a tremendous stimulus for further research into this field. Isogeometric analysis is being applied to a growing number of problems, increasing the insight in the performance of isogeometric discretizations. Simultaneously, research on the approximation properties of splines increases the fundamental understanding of these basis functions. Also, research on spline technologies has entered the realm of analysis. This research, traditionally carried out in the context of computer aided geometric design (CAGD), focuses on the development of spline technologies that satisfy the (sometimes conflicting) requirements of CAGD and analysis. The formulation of an element interface to splines by means of Bézier extraction is an example of this kind of research. The development of efficient and robust refinement schemes is another research topic. The latter is closely related to the research on the mathematical properties of splines.
This mini-symposium aims at giving an overview of recent advancements made in isogeometric analysis. This includes both research on novel applications, and fundamental research on spline technologies.