Übung 7: Einfache räumliche Struktur

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1 FEM Übung 7: Einfache räumliche Struktur Introduction to 3-Dimensional Elements You can use three-dimensional elements, commonly referred to as solid elements, to model structures that can t be modeled using beam or plate elements. For instance, a solid element is used to model an engine block because of the block s three-dimensional nature. If however, you re creating a model of the automobile hood, the best choice is one of the plate elements. This chapter describes the following elements: CHEXA, CPENTA, CTETRA CRAC3D (three-dimensional crack tip element) CTRIAX6 (axisymmetric element that s used for axisymmetric analysis only) Solid elements have only translational degrees of freedom. No rotational DOFs are used to define the solid elements. FEM Folie 7-1 FHA / FM / TH 2007/11

2 FEM Übung 7: Einfache räumliche Struktur Solid Elements (CTETRA, CPENTA, CHEXA) NX Nastran includes three different solid polyhedron elements which are defined on the following Bulk Data entries: 1. CTETRA Four-sided solid (pyramid) element with 4 to 10 grid points 2. CPENTA Five-sided solid (wedge) element with 6 to 15 grid points 3. CHEXA Six-sided solid (brick) element with 8 to 20 grid points These elements differ from each other primarily in the number of faces and in the number of connected grid points. You can use these elements with all other NX Nastran elements except the axisymmetric elements. Connections are made only to displacement degrees-of-freedom at the grid points. The CHEXA element is the most commonly used solid element in the NX Nastran element library. The CPENTA and CTETRA elements are used mainly for mesh transitions and in areas where the CHEXA element is too distorted. FEM Folie 7-2 FHA / FM / TH 2007/11

3 FEM Übung 7: Einfache räumliche Struktur Solid Element Integration Types The CHEXA and the CPENTA are modified isoparametric elements that use selective integration points for different components of strain. In addition to the standard isoparametric integration, there are two different networks of integration points available, depending on whether the element has midside nodes. FEM Folie 7-3 FHA / FM / TH 2007/11

4 FEM Übung 7: Einfache räumliche Struktur Four-Sided Solid Element (CTETRA) The CTETRA element is an isoparametric tetrahedron element with four vertex nodes and up to six additional midside nodes. If you use midside nodes, you should include all six nodes. The accuracy of the element degrades if some but not all the edge grid points are used. The CTETRA solid element is used widely to model complicated systems (i.e. extrusions with many sharp turns and fillets, turbine blades). The element has a distinct advantage over the CHEXA when the geometry has sharp corners as you can have CTETRAs that are much better shaped than CHEXAs. However, you should always use CTETRAs with ten grid points for all structural simulations (e.g. solving for displacement and stress). The CTETRA with four grid points is overly stiff for these applications. In general, you should minimize your use of the 4-noded CTETRA, especially in the areas of high stress. However, CTETRAs with four grid points are acceptable for heat transfer applications. NX Nastran calculates element stresses at the element s center and extrapolates them out to the corner grid points. The element s connection geometry is shown below. FEM Folie 7-4 FHA / FM / TH 2007/11

5 FEM Übung 7: Einfache räumliche Struktur FEM Folie 7-5 FHA / FM / TH 2007/11

6 FEM Übung 7: Einfache räumliche Struktur The CTETRA element coordinate system is derived from the three vectors R, S, and T which join the midpoints of opposite edges. The R vector joins the midpoints of edges G1-G2 and G3-G4. The S vector joins the midpoints of edges G1-G3 and G2-G4. The T vector joins the midpoints of edges G1-G4 and G2-G3. The origin of the coordinate system is located at G1. The element coordinate system is chosen as close as possible to the R, S, and T vectors and points in the same general direction. FEM Folie 7-6 FHA / FM / TH 2007/11

7 FEM Übung 7: Einfache räumliche Struktur FEM Folie 7-7 FHA / FM / TH 2007/11

8 FEM Übung 7: Einfache räumliche Struktur Geometrie FEM Folie 7-8 FHA / FM / TH 2007/11

9 FEM Übung 7: Einfache räumliche Struktur Geometrie Übernahme aus CAD-System: Solid Edge Part-Datei Parasolid ACIS STEP IGES File - Preferences File Import - Geometry FEM Folie 7-9

10 FEM Übung 7: Einfache räumliche Struktur Geometrie FEM Folie 7-10 FHA / FM / TH 2007/11

11 FEM Übung 7: Einfache räumliche Struktur Geometrie Workplane Rotate (um z-achse; 90 ) FEM Folie 7-11

12 FEM Übung 7: Einfache räumliche Struktur Geometrie FEM Folie 7-12

13 FEM Übung 7: Einfache räumliche Struktur Geometrie FEM Folie 7-13 FHA / FM / TH 2007/11

14 FEM Übung 7: Einfache räumliche Struktur Geometrie FEM Folie 7-14 FHA / FM / TH 2007/11

15 FEM Übung 7: Einfache räumliche Struktur Geometrie FEM Folie 7-15

16 FEM Übung 7: Einfache räumliche Struktur Geometrie Bolzenlänge 60 mm Bolzen einfügen FEM Folie 7-16

17 FEM Übung 7: Einfache räumliche Struktur Geometrie/Groups Bolzen und Berührflächen gruppieren Group Set Group Solid Group Surface On Solid (Bolzenfläche) Group Surface (Berührflächen) View Select Model Data (Group) FEM Folie 7-17

18 FEM Übung 7: Einfache räumliche Struktur Connect Connect - Surfaces... FEM Folie 7-18

19 FEM Übung 7: Einfache räumliche Struktur Material/Property FEM Folie 7-19

20 FEM Übung 7: Einfache räumliche Struktur Vernetzung FEM Folie 7-20

21 FEM Übung 7: Einfache räumliche Struktur Vernetzung FEM Folie 7-21

22 FEM Übung 7: Einfache räumliche Struktur Belastung Bolzenaussenflächen: je N in x-richtung FEM Folie 7-22

23 FEM Übung 7: Einfache räumliche Struktur Lagerung FEM Folie 7-23

24 FEM Übung 7: Einfache räumliche Struktur Ergebnisse FEM Folie 7-24

25 FEM Übung 7: Einfache räumliche Struktur Ergebnisse FEM Folie 7-25

26 FEM Übung 7: Einfache räumliche Struktur Ergebnisse FEM Folie 7-26

27 FEM Übung 7: Einfache räumliche Struktur Symmetrie Geometry Solid Slice... FEM Folie 7-27

28 FEM Starrkörperverschiebungen Beispiel: y x-lager 1 2 F x2 x F x2 = E = A = 1 [F x1 F y1 F x v u 2 F y2]=[ ] [u1 2] v FEM Folie 7-28 FHA / FM / TH 2007/11

29 FEM Starrkörperverschiebungen reduziertes System: u 1 = 0; [F x1 F y1 F x v u 2 F y2]=[ ] [u1 2] v [ 0 1 0] [ ] [v1 = ] 0 0 v u 2 Gleichungssystem nicht lösbar, da Determinante gleich Null FEM Folie 7-29 FHA / FM / TH 2007/11

30 FEM Starrkörperverschiebungen zusätzliche Lagerung in den Knoten 1 und 2 in y-richtung: [ 0 1 0] [ ] [v1 = u 2] 2 v u 2 = 1; FEM Folie 7-30 FHA / FM / TH 2007/11

31 FEM Starrkörperverschiebungen Die Struktur muss immer so gelagert sein, dass unabhängig von der Belastung keine Starrkörperverschiebungen möglich sind. FEM Folie 7-31 FHA / FM / TH 2007/11