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Introduction to Isogeometric Analysis


  • Dr. Ste­fan Hart­mann


  • $350
  • $175 for students

What's Included

  • One day of in­struc­tion
  • Class notes

Introduction to Isogeometric Analysis


  • Equiv­a­lent knowl­edge to an in­tro­duc­to­ry class in LS-DY­NA® is rec­om­mend­ed.


This class pro­vides an in­tro­duc­tion to Iso­ge­o­met­ric Analy­sis (IGA) with Non-Uni­form Ra­tio­nal B-Splines (NURBS) in LS-DY­NA. As a part of this class you will learn how to switch from low-or­der fi­nite el­e­ments to IGA. Some the­o­ret­i­cal back­ground about IGA and NURBS will be pre­sent­ed be­fore ex­plor­ing the cur­rent ca­pa­bil­i­ties in LS-DY­NA. Set­ting up a suit­able mod­el from some CAD-file us­ing LS-Pre­Post® will al­so be cov­ered. The class will deal with both shell and sol­id el­e­ments with an em­pha­sis on shell el­e­ments.


  1. In­tro­duc­tion and mo­ti­va­tion
  2. The­o­ret­i­cal back­ground
    1. B-Splines
    2. NURBS
    3. Oth­er CAD-de­scrip­tions
  3. NURBS sur­faces
    1. Untrimmed NURBS patch­es
    2. Trimmed NURBS patch­es
    3. Bound­ary Rep­re­sen­ta­tion in CAD
  4. NURBS-based shell for­mu­la­tions
    1. Reiss­ner-Mindlin shell
    2. Kirch­hoff-Love shell
    3. Hy­brid shell
  5. Ap­pli­ca­tion of bound­ary con­di­tions
    1. In­ter­po­la­tion nodes and el­e­ments
    2. Con­tact with in­ter­po­la­tion el­e­ments
    3. Con­tact with NURBS el­e­ments
    4. Spot­weld mod­el­ing
  6. Join­ing of patch­es
    1. Match­ing untrimmed patch­es
    2. Non-match­ing untrimmed patch­es
    3. Trimmed patch­es
  7. Mod­el set­up
    1. Im­port IGES/­STEP file and cre­ate NURBS patch­es
    2. Nec­es­sary key­words
  8. Post-pro­cess­ing
    1. Via in­ter­po­la­tion el­e­ments
    2. IGAPLOT-file
  9. Ex­am­ples
  10. NURBS-based solids in LS-DY­NA
    1. Cur­rent ca­pa­bil­i­ties
    2. Nec­es­sary key­words
    3. Mod­el set­up
    4. Ex­am­ples
  11. Bezi­er-Ex­trac­tion in­ter­face
  12. Dis­cus­sion and out­look