Valid from: Spring 2014
Decided by: FN1/Anders Gustafsson
Date of establishment: 2014-04-22
Division: Numerical Analysis
Course type: Third-cycle course
Teaching language: English
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.
Knowledge and Understanding
For a passing grade the doctoral student must
Competences and Skills
For a passing grade the doctoral student must
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.
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.
Cottrell, J.A., Hughes, T.J.R. & Bazilevs, Y.: Isogeometric Analysis: Toward Integration of CADF and FEA. Wiley, 2009. ISBN 9780470748732.
Types of instruction: Lectures, exercises, project, miscellaneous. Presentations by the participants.
Examination formats: Oral exam, written report
Grading scale: Failed, pass
Examiner:
Admission requirements: 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.
Course coordinators:
Web page: http://ctr.maths.lu.se/na/courses/FMNN182/