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

FMN001F, 7.5 högskolepoäng

Gäller från och med: Spring 2014
Beslutad av: FN1/Anders Gustafsson
Datum för fastställande: 2014-04-22

Allmänna uppgifter

Avdelning: Numerical Analysis
Kurstyp: Ren forskarutbildningskurs
Undervisningsspråk: English

Syfte

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.

Mål

Kunskap och förståelse

För godkänd kurs skall doktoranden

• 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

Färdighet och förmåga

För godkänd kurs skall doktoranden

• 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

Värderingsförmåga och förhållningssätt

För godkänd kurs skall doktoranden be able to decide on the fundamental properties of a NURBS mesh (degree, knots, continuity) in order to accurately model the geometry.

Kursinnehåll

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.

Kurslitteratur

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

Kursens undervisningsformer

Undervisningsformer: Föreläsningar, övningar, projekt, övrigt. Presentations by the participants.

Kursens examination

Examinationsformer: Muntlig tentamen, skriftlig rapport
Betygsskala: Underkänd, godkänd
Examinator:

Antagningsuppgifter

Förkunskapskrav: Basic knowledge of linear algebra, calculus of one and several variables, and differential equations.
Förutsatta förkunskaper: Basic knowledge of the finite element method is recommended.

Kurstillfällesinformation

Kontaktinformation och övrigt

Kursansvariga:
Hemsida: http://ctr.maths.lu.se/na/courses/FMNN182/