Third-Cycle Courses

Faculty of Engineering | Lund University

Details for the Course Syllabus for Course FMN001F valid from Spring 2014

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  • 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.
  • 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
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.
Selection Criteria
  • 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
Administrative Information
  •  -04-22
  • FN1/Anders Gustafsson

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