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Detaljer för kurs FMN001F Isogemetrisk analys: CAD i FEM

Utskriftsvänlig visning

Allmänt
  • FMN001F
  • Tillfällig
Kursnamn
  • Isogeometric Analysis: CAD in FEM
Kursomfattning
  • 7,5
Undervisningsform
  • Ren forskarutbildningskurs
Administrativ information
  • 7154 (Matematikcentrum (inst LTH) / Numerisk analys (LTH))
  •  -04-22
  • FN1/Anders Gustafsson

Aktuell fastställd kursplan

Allmänt
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.
Innehåll
  • 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.
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.
Undervisningsformer
  • Föreläsningar
  • övningar
  • Projekt
  • övrigt
  • Presentations by the participants.
Examinationsformer
  • Muntlig tentamen
  • Skriftlig rapport
  • Underkänd, godkänd
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.
Urvalskriterier
Litteratur
  • Cottrell, J.A., Hughes, T.J.R. & Bazilevs, Y.: Isogeometric Analysis: Toward Integration of CADF and FEA. Wiley, 2009. ISBN 9780470748732.
Övrig information
Kurskod
  • FMN001F
Administrativ information
  •  -04-22
  • FN1/Anders Gustafsson

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VT 2014 2014‑03‑25 10:45:04 2014‑03‑25 10:48:05 2014‑04‑22

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