I³MS - Reali Seminar
Prof. Dr. Alessandro Reali - Isogeometric Analysis: Some Recent Advances and Applications
Computational Mechanics & Advanced Materials Group, University of Pavia
Isogeometric Analysis (IGA) is a recent simulation framework, originally proposed by T.J.R. Hughes and coworkers in 2005, to bridge the gap between Computational Mechanics and Computer Aided Design (CAD). The basic IGA paradigm consists of adopting the same basis functions used for geometry representations in CAD systems - such as, e.g., Non-Uniform Rational B-Splines (NURBS) - for the approximation of field variables, in an isoparametric fashion. This leads to a cost-saving simplification of the typically expensive mesh generation and refinement processes required by standard finite element analysis. In addition, thanks to the high-regularity properties of its basis functions, IGA has shown a better accuracy per-degree-of-freedom and an enhanced robustness with respect to standard finite elements in a number of applications ranging from solids and structures to fluids, opening also the door to geometrically flexible discretizations of higher-order partial differential equations in primal form, as well as to highly efficient collocation methods. This lecture aims at illustrating the unique potential of IGA through some convincing applications, mainly belonging to the field of solid and structural mechanics, where the superior results that can be provided by IGA with respect to standard finite elements are clearly pointed out. In particular, after a brief introduction about the IGA approximation properties of structural vibrations, the application to a real-life case, the so-called NASA “Aluminum Testbed Cylinder”, is shown along with comparisons with experimental results. As a further example, the demanding explicit structural dynamics simulation of a patient-specific aortic valve, modeled by nonlinear hyper-elastic shells and involving large deformations and contact, is presented and carefully analyzed in terms of accuracy and efficiency. Such results are also complemented by an impressive example of fluid-structure interaction (FSI) simulation of an aortic valve prosthesis, based on an ``immersed’’ IGA method. As a third representative case study, the bending behavior of a complex structure like a shape memory alloy stent is simulated in the large deformation regime, with particular attention to a correct modeling of buckling phenomena. Convincing preliminary results about the extension to the complete simulation of the stent implantation process are also shown. The lecture is finally concluded by a brief presentation of some further works and ideas in progress, with a special focus on so-called IGA collocation methods.