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TYPICAL ELEMENTS

Triangular shell element6 D.O.F. per node

Tetrahedral solid element3 D.O.F. per node

First order elements

Linear displacement distributionConstant stress distribution

Second order elements

Second order displacement distributionLinear stress distribution

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TWO POSSIBLE REPRESENTATIONS OF A PLATE

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CAN YOU IDENTIFY THESE ELEMENTS?

Note: all these elements would be way too large for analysis

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Draft Quality – first order element

High Quality – second order element

SW TERMINOLOGY

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FINITE ELEMENT MESH

Mesh compatibility

Mesh quality

Mesh adequacy

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MESH COMPATIBILITY

Compatible elements

The same displacement shape function along edge 1 and edge 2

Incompatible elements

The same displacement shape function along edge 1 and edge 2

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Model of flat bar under tension. There is an incompatibility along the mid-line between the left and the right side of the model.

The same model after analysis. Due to incompatibility a gap has formed along the mid-line.

MESH COMPATIBILITY

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Tetrahedral solid elements and hexahedral solid elements combined in one model.

Hexahedral solid elements

Tetrahedral solid elements

MESH COMPATIBILITY

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Shell elements and solid elements combined in one model.

Shell elements are attached to solid elements by links constraining their translational D.O.F. to D.O.F. of solid

elements and suppressing their rotational D.O.F. This way nodal rotations of shells are eliminated and nodal

translations have to follow nodal translations of solids.

Unintentional hinge will form along connection to solids if rotational D.O.F. of shells are not suppressed.

Exaggerated stress concentration may appear along the link lines.

MESH COMPATIBILITY

Shell elements

Solidelements

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Elements before mapping Elements after mapping

MESH QUALITY

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MESH QUALITY

aspect ratio

angular distortion ( skew )

angular distortion ( taper )

curvature distortion

midsize node position

warpage

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Element distortion: aspect ratio

Element distortion: warping

MESH QUALITY

13Element distortion: tangent edges

MESH QUALITY

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MESH ADEQUACY

This stress distribution need to be modeled

This is what is modeled with one layer of first order elements

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c a n t i l e v e r b e a m , m o d e l 1t e r r i b l y b a d

c a n t i l e v e r b e a m , m o d e l 2a l s o t e r r i b l y b a d

c a n t i l e v e r b e a m m o d e l 3a g o o d b e g i n n i n g !

c a n t i l e v e r b e a m , m o d e l 4a n a c c e p t a b l e m o d e l

cantilever beam size: 10" x 1" x 0.1"modulus of elasticity: 30,000,000 PSIload: 150 lb.beam theory maximal deflection: f = 0.2"beam theory maximal stress: = 90,000 PSI

our definition of the discretization error : ( beam theory result - FEA result ) / beam theory result

model #

FEA deflection

[in]

deflection error [%]

FEA stress [ PSI ]

stress error [%]

1 0.1358 32 1,500 98

2 0.1791 10 39,713 56

3 0.1950 2.5 65,275 27

4 0.1996 0.2 80,687 10

MESH ADEQUACY

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MESH ADEQUACY

Two layers of second order solid elements are generally recommended for modeling bending.

Shell elements adequately model bending.

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MESH ADEQUACY

Incorrect shell elements meshing using automatically generated mid-surface