Novel Methods for Isogeometric Shape Modeling and Numerical Simulation
Prof. Dr. Gang Xu
Department of Computer Science and Technology
Hangzhou Dianzi University
The isogeometric analysis approach originally proposed by Hughes et al. provides a possibility to overcome the gap between CAD and finite element analysis by using the same mathematical representation based on NURBS for all design and analysis tasks. This framework allows to compute the analysis results on the exact CAD geometry rather than a discrete mesh geometry, to obtain a more accurate solution by high-order approximation, to reduce spurious numerical sources of noise that deteriorate convergence, and to avoid data exchanges between the design and analysis phases. From the viewpoint of shape modeling, some geometric-modeling issues for isogeometric analysis should be investigated. In this tutorial, the concept of isogeometric analysis, its implementation and recent advances in engineering applications will be firstly introduced; then our recent work on geometric-modeling issues, such as analysis-suitable planar and volumetric parameterization of computational domain, r-refinement in isogeometric analysis, analysis-suitable spline models, and the high-order visualization tools for isogeometric analysis will be presented; finally, some novel numerical simulation methods with isogeometric analysis will be also introduced, including the precomputed isogeometric analysis for CAD models with consistent volumetric parameterization, isogeometric analysis with reproducing-kernel triangular B-splines and an extension of isogeometric analysis approach by representing the geometry and solution field with different spline models.