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# Details for Course FMN001F Isogeometric Analysis: CAD in FEM

General
• FMN001F
• Temporary
Course Name
• Isogeometric Analysis: CAD in FEM
Course Extent
• 7.5
Type of Instruction
• Third-cycle course
• 7154 (Centre of Mathematical Sciences / Numerical Analysis)
•  -04-22
• FN1/Anders Gustafsson

## Current Established Course Syllabus

General
Aim
• Isogeometric analysis carries over Computer Aided Design (CAD) geometry into the Finite Element Method (FEM), by replacing the classical basis functions of FEM with B-splines and NURBS (Non-Uniform Rational B-Splines). The reason behind this recently developed technique is to enhance accuracy by allowing FEM simulations directly on CAD models. Applications are especially important in areas where higher-order smoothness is required, such as shell theory, cohesive-zone models in failure mechanics, and free-boundary problems. The course is relevant for PhD-students within numerical analysis that would like to pursue research within the FEM or would like to broaden their competence and to students in other areas who would like to use the FEM in their research.
Contents
• B-splines. Non-Uniform Rational B-splines. Basis functions, properties and construction. Knot refinement. Multiple patches.
NURBS meshes. Boundary value problems. Galerkin methods. Boundary conditions. The finite element method.
Comparison of finite elements and isogeometric analysis. The equations of elastostatics. Modelling of shells.
Knowledge and Understanding
• For a passing grade the doctoral student must
• have an understanding of how geometry and analysis interact in solving partial differential equations with the finite element method
have an understanding of Non-Uniform Rational B-Splines (NURBS) and the properties of their basis functions
have an understanding of the difference between isogeometric analysis and finite elements

Competences and Skills
• For a passing grade the doctoral student must
• demonstrate how to generate a NURBS element (curve, surface or solid)
be able to construct a NURBS mesh for a Galerkin method
be able to write a simple code to solve a linear elasticity problem using isogeometric analysis
Judgement and Approach
• For a passing grade the doctoral student must
• be able to decide on the fundamental properties of a NURBS mesh (degree, knots, continuity) in order to accurately model the geometry.
Types of Instruction
• Lectures
• Exercises
• Project
• Miscellaneous
• Presentations by the participants.
Examination Formats
• Oral exam
• Written report
• Failed, pass
• Basic knowledge of linear algebra, calculus of one and several variables, and differential equations.
Assumed Prior Knowledge
• Basic knowledge of the finite element method is recommended.
Selection Criteria
Literature
• Cottrell, J.A., Hughes, T.J.R. & Bazilevs, Y.: Isogeometric Analysis: Toward Integration of CADF and FEA. Wiley, 2009. ISBN 9780470748732.
Further Information
Course code
• FMN001F
•  -04-22
• FN1/Anders Gustafsson

## All Established Course Syllabi

1 course syllabus.

Valid from First hand in Second hand in Established
Spring 2014 2014‑03‑25 10:45:04 2014‑03‑25 10:48:05 2014‑04‑22

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