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Isogeometric Analysis

General

Solution to Plateau's Problem (Exercise 10).

Solution to Plateau's Problem (Exercise 10)

• The course will take place on Tuesdays, 10:15 to 12:45 in room 115 of the Rogowski building (Schinkelstr. 2).

• It will consist of a lecture of 1.5 hours and a subsequent exercise of 45 minutes. During the exercise, an IGA code will be programmed in Matlab. The lecture language is English.

• Workload: 6CP (V2/Ü1)

• Campus: 16ws-41659

• Instructor: Dr.-Ing. Stefanie Elgeti

• Assistant: Florian Zwicke, M.Sc.

Course description

The course will give an introduction to the concept of Isogeometric Analysis (IGA), particularly in comparison to the classical Finite Element Method. In Isogeometric Analysis, the interpolation is performed using non-uniform rational B-splines (NURBS). As NURBS are also the basis of CAD-models, the idea is to be able to perform Finite Element simulations directly on CAD-models, avoiding a separate meshing step. The new nature of the interpolation requires the adaption of the classical Finite Element Method, e.g. mesh refinement strategies specific to IGA need to be developed. During the course, we will cover the application of IGA to structural mechanics, heat transfer and fluid mechanics. In the context of fluid mechanics, a comparison to the related topic of “NURBS-Enhanced Finite Elements” will be discussed.

Course objectives

Graduate students in the course will:

• Become acquainted with the method of IGA and learn about the difficulties which come about with the different areas of application.

• Program their own small IGA code as a means of gaining experience with the method.

• Become familiar with the method of “NURBS Enhanced Finite Elements” as an alternative to IGA in the fluids context.

Recommended reading

• J. A. Cottrell, T. Hughes, Y. Bazilevs: Isogeometric Analysis - Toward Integration of CAD and FEA, Wiley, 2009

• Sevilla, R. Fernandez-Mendez, S. and Huerta A.: 3D NURBS-Enhanced Finite Element Method (NEFEM), International Journal for Numerical Methods in Engineering, 88 (2), 103-125, 2011

Exercises

• For the exercise, you will need access to Matlab. If you don't have it available yet, please consult this page.

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Homework assignments

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