Course Syllabus for

# Isogeometric Analysis: CAD in FEM Isogemetrisk analys: CAD i FEM

## FMN001F, 7.5 credits

Valid from: Spring 2014
Decided by: FN1/Anders Gustafsson
Date of establishment: 2014-04-22

## General Information

Division: Numerical Analysis
Course type: Third-cycle course
Teaching language: English

## 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.

## Goals

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.

## Course 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.

## Course Literature

Cottrell, J.A., Hughes, T.J.R. & Bazilevs, Y.: Isogeometric Analysis: Toward Integration of CADF and FEA. Wiley, 2009. ISBN 9780470748732.

## Instruction Details

Types of instruction: Lectures, exercises, project, miscellaneous. Presentations by the participants.

## Examination Details

Examination formats: Oral exam, written report
Grading scale: Failed, pass
Examiner: