Isogeometric analysis

Isogeometric Analysis (IGA) is a numerical method for approximate solutions to boundary-value problems in science and engineering. Its peculiarity is that the numerical approximation uses the same basic functions that are used to construct a CAD geometric model (Non-uniform rational B-spline (NURBS) are standard in contemporary CAD industry). In this way, it is possible to perform analysis directly on CAD model without meshing. The goal of the course is to acquaint students with the concept of isogeometric analysis, specifically in comparison to the classical Finite Element Method. Student will gain operational knowledge through programming of small IGA code and learn about problems that arise in implementation of IGA.

After completing the course, students gain practical and theoretical knowledge that will serve as a basis for further research and practical work in the field. By programming small IGA code students obtain working experience in IGA implementation and foundation for further upgrade and practical implementation of the new achievments in IGA in own code. Students will learn about possibilities of increase of NURBS basis functions degree and advantages that this property offers in the field of mechanics of elastic bodies.

- Introduction and overview of IGA development - Geometrical foundations – NURBS geometry - Equations of elastomechanics - Approximation methods - Interpolation functions in conventional FEM - Domain discretization in IGA - Boundary conditions in IGA - Quadrature in IGA - Multipatch geometries - Modern alternatives to NURBS basis functions in IGA

- Becoming familiar with the methodology of computer implementation of IGA through programming own IGA code - Modeling of NURBS geometries - Solving of selected problems in elastomechanics - Comparison of the obtained results with the results of commercial software packages for finite element analysis.

No obligatory prerequisites. Good knowledge of Matlab is desirable.

1. Lecture materials (written excerpts of the lectures, problem formulations, guidelines for solving the problems), DVL

Total assigned hours: 65

New material: 35
Elaboration and examples (recapitulation): 15

Auditory exercises: 0
Laboratory exercises: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 0
Review and grading of lab reports: 0
Review and grading of seminar papers: 0
Review and grading of the project: 10
Test: 0
Test: 0
Final exam: 5

Activity during lectures: 0
Test/test: 0
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 0
Project: 70
Final exam: 30
Requirement for taking the exam (required number of points): 70

Cottrell J.A., Hughes T.J.R., Bazilevs Y., 2009, Isogeometric Analysis: Toward Integration of CAD and FEA, John Wiley & Sons, Chichester; Piegl L., Tiller W., 1997, The NURBS Book, Springer-Verlag New York, New York; Rogers D., 2001, An Introduction to NURBS With Historical Perspective, Morgan Kaufmann Publishers, San Francisco; Hughes TJR, 1987, The finite element method. Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Inc., Englewood Cliffs, New Jersey ; Lecture Notes and Lecture Slides