Reference : Generalizing the isogeometric concept: weakening the tight coupling between geometry ...
Scientific Presentations in Universities or Research Centers : Scientific presentation in universities or research centers
Engineering, computing & technology : Multidisciplinary, general & others
Computational Sciences
http://hdl.handle.net/10993/27734
Generalizing the isogeometric concept: weakening the tight coupling between geometry and simulation in IGA
English
Tomar, Satyendra mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
Atroshchenko, Elena mailto [University of Chile > Department of Mechanical Engineering]
Xu, Gang mailto [Hangzhou Dianzi University]
Bordas, Stéphane mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
2-Jun-2016
24
International
High-Order Finite Element and Isogeometric Methods 2016
30.05.2016 - 02.06.2016
Israel Science Foundation, and Ben Gurion University of the Negev
Jerusalem
Israel
[en] Isogeometric analysis ; Sub-parametric ; Super-parametric
[en] In the standard paradigm of isogeometric analysis [2, 1], the geometry and the simulation spaces are tightly integrated, i.e. the non-uniform rational B-splines (NURBS) space, which is used for the geometry representation of the domain, is also employed for the numerical solution of the problem over the domain. However, in certain situations, such as, when the geometry of the domain can be represented by low order NURBS but the numerical solution can be obtained with improved accuracy by using NURBS of order higher than that required for the geometry; or in the shape and topology optimization where the constraint of using the same space for the geometry and the numerical solution is not favorable, this tight coupling is disadvantageous.
Therefore, we study the effect of decoupling the spaces for the geometry representation and the numerical solution, though still using the prevalent functions in CAD/CAGD. To begin with, we perform the patch tests on various combinations of polynomial degree, geometry type, and various cases of varying degrees and control variables between the geometry and the numerical solution. This shows that certain cases, perhaps intuitive, should be avoided in practice because patch test fails. The above-mentioned situations are further explored with some numerical examples, which shows that weakening the tight coupling between geometry and simulation offers more flexibility in choosing the numerical solution spaces. [1] J. Cottrell, T.J.R. Hughes, and Y. Bazilevs. Isogeometric Analysis: Toward Integration of CAD and FEA, volume 80. Wiley, Chichester, 2009.
[2] T.J.R. Hughes, J. Cottrell, and Y. Bazilevs. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering, 194:4135–4195, 2005.
Researchers ; Professionals ; Students
http://hdl.handle.net/10993/27734
FP7 ; 289361 - INSIST - Integrating Numerical Simulation and Geometric DesignTechnology

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