Übung 7: Einfache räumliche Strukturthalhof/downloads/ueb07folien.pdf · FEM Übung 7: Einfache räumliche Struktur FEM Folie 7- 4 Four-Sided Solid Element (CTETRA) The CTETRA element

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FEM Übung 7: Einfache räumliche Struktur

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Introduction to 3-Dimensional Elements

You can use three-dimensional elements, commonly referred to as solid elements, tomodel structures that can’t be modeled using beam or plate elements. For instance, asolid 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 areused to define the solid elements.

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Solid Elements (CTETRA, CPENTA, CHEXA)

NX Nastran includes three different solid polyhedron elements which are defined onthe following Bulk Data entries:

1. CTETRA – Four-sided solid (pyramid) element with 4 to 10 grid points2. CPENTA – Five-sided solid (wedge) element with 6 to 15 grid points3. 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 thenumber of connected grid points. You can use these elements with all other NXNastran elements except the axisymmetric elements. Connections are made only todisplacement degrees-of-freedom at the grid points.

The CHEXA element is the most commonly used solid element in the NX Nastranelement library. The CPENTA and CTETRA elements are used mainly for meshtransitions and in areas where the CHEXA element is too distorted.

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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.

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Four-Sided Solid Element (CTETRA)

The CTETRA element is an isoparametric tetrahedron element with four vertex nodesand up to six additional midside nodes. If you use midside nodes, you shouldinclude all six nodes. The accuracy of the element degrades if some but not all theedge 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 adistinct advantage over the CHEXA when the geometry has sharp corners as you canhave CTETRAs that are much better shaped than CHEXAs. However, you shouldalways use CTETRAs with ten grid points for all structural simulations (e.g. solvingfor displacement and stress). The CTETRA with four grid points is overly stiff forthese applications. In general, you should minimize your use of the 4-nodedCTETRA, especially in the areas of high stress. However, CTETRAs with four gridpoints 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.

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The CTETRA element coordinate system is derived from the three vectors R, S, and Twhich 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 systemis chosen as close as possible to the R, S, and T vectors and points in the same general direction.

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FEM Übung 7: Einfache räumliche Struktur Geometrie

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10

20

40 40

1050 25

25

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Übernahme aus CAD-System:

● Solid Edge Part-Datei● Parasolid● ACIS● STEP● IGES

File - Preferences

File – Import - Geometry

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FEM Folie 7- 11

Workplane – Rotate (um z-Achse; 90°)

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Bolzen einfügen

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Bolzenlänge 60 mm

FEM Übung 7: Einfache räumliche Struktur Geometrie/Groups

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Group – SetGroup – SolidGroup – Surface – On Solid (Bolzenfläche)Group – Surface (Berührflächen)

Bolzen und Berührflächen gruppieren

View – Select – Model Data (Group)

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FEM Übung 7: Einfache räumliche Struktur Connect

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Connect - Surfaces...

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FEM Übung 7: Einfache räumliche Struktur Material/Property


FEM Übung 7: Einfache räumliche Struktur Vernetzung


FEM Übung 7: Einfache räumliche Struktur Vernetzung


FEM Übung 7: Einfache räumliche Struktur Belastung

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Bolzenaussenflächen: je -15 000 N in x-Richtung

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FEM Übung 7: Einfache räumliche Struktur Lagerung


FEM Übung 7: Einfache räumliche Struktur Ergebnisse






FEM Übung 7: Einfache räumliche Struktur Symmetrie

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Geometry – Solid – Slice ...

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FEM Starrkörperverschiebungen

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Beispiel:

Fx21

22

x-Lager

x

y

Fx2

= E = A = 1

[F x1F y1

F x2F y2]=[1 0 −1 0

0 0 0 0−1 0 1 00 0 0 0]⋅[u1

v1

u2

v2]

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[F x1F y1

F x2F y2]=[1 0 −1 0

0 0 0 0−1 0 1 00 0 0 0]⋅[u1

v1

u2

v2]

reduziertes System: u1 = 0;

[010]=[0 0 00 1 00 0 0]⋅[v1

u2

v2] Gleichungssystem nicht lösbar,

da Determinante gleich Null

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[010]=[0 0 00 1 00 0 0]⋅[v1

u2

v2]

zusätzliche Lagerung in den Knoten 1 und 2 in y-Richtung:

u2 = 1;

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Die Struktur muss immer so gelagert sein, dass

unabhängig von der Belastung

keine Starrkörperverschiebungen möglich sind.

Documents

Übung 7: Einfache räumliche Strukturthalhof/downloads/ueb07folien.pdf · FEM Übung 7: Einfache räumliche Struktur FEM Folie 7- 4 Four-Sided Solid Element (CTETRA) The CTETRA element