I am looking to start working with the isogeometric method to analyze mechanical behavior such as beam, plate, shell and other structures of complex shapes.
can you help me by giving me simple examples in this method and with articles and books that have explanations and applications?
what do you suggest to me and thank you in advance?
The best book you can borrow from your Library :https://www.dymocks.com.au/book/isogeometric-analysis-and-applications-2014-by-bert-juttler-and-bernd-simeon-9783319794709?utm_source=googleps&gclid=EAIaIQobChMI5_jdwvfc5gIVwRErCh3j8wIbEAYYBCABEgIUcvD_BwE
Prof. Thomas j.r. Hughes is an expert in isogeometric analysis. Just try to flow his works in this regard. Have a look hier
https://youtu.be/Vwl69Ds69y0
The following some references
(1) Computational Methods for Fracture in Porous Media: Isogeometric and Extended Finite Element Methods
Elsevier
René de Borst
2)Precursors of Isogeometric Analysis: Finite Elements, Boundary Elements, and Collocation Methods
Springer International PublishingChristopher
G. Provatidis (3) Isogeometric Methods for Numerical Simulation
Springer-Verlag
WienGernot Beer, Stéphane Bordas (eds.)
Dr.@ Muhammad Ali
Thank you, it is a very interesting book, but it does not give us for their simple examples: method of deep resolution and explanation for mathematical and analytical formulation.
Dear Mokhtar Nebab ,
As an introduction to IgA, you can have a look at this book: https://www.wiley.com/en-us/Isogeometric+Analysis%3A+Toward+Integration+of+CAD+and+FEA-p-9780470748732. It is quite old, but the basics with splines etc. are covered quite nicely.
Regarding shells, I recommend the work of Josef Kiendl. In his PhD thesis, he also gave fundamentals of IgA:
https://mediatum.ub.tum.de/doc/1002634/464162.pdf
Regarding beams, there are less references that I recommend. There is some work of Oliver Weeger
e.g. Weeger, O., Wever, U. & Simeon, B. Isogeometric analysis of nonlinear Euler-Bernoulli beam vibrations. Nonlinear Dyn. (2013). doi:10.1007/s11071-013-0755-5
But some beam formulations are a little more complicated when they include the twisting of the beam
e.g. Weeger, O., Narayanan, B. & Dunn, M. L. Isogeometric shape optimization of nonlinear, curved 3D beams and beam structures. Comput. Methods Appl. Mech. Eng. 345, 26–51 (2019).
I, myself, studied the basics of IgA in my MSc. thesis work and applied this to a simple beam formulation. Looking back, it is not the most generic formulation, but it could help you. I also studied the shell formulation.
https://repository.tudelft.nl/islandora/object/uuid%3A56c0cc91-643d-4817-9702-93fedce5fd78?collection=education
Hope this helps you.
Best,
Hugo
- Badges
- Science topic
- Similar topics
- Mathematics
- Applied Mathematics