Triangular shell element
6 D.O.F. per node
Tetrahedral solid element
3 D.O.F. per node
First order elements
Linear displacement distribution
Constant stress distribution
Second order elements
Second order displacement distribution
Linear stress distribution
1

2

3

Draft Quality – first order element
High Quality – second order element
4

5

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
6

MESH COMPATIBILITY
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.
7

MESH COMPATIBILITY
Tetrahedral solid elements
Hexahedral solid elements
Tetrahedral solid elements and hexahedral solid elements combined in one model.
8

Solid elements
MESH COMPATIBILITY
Shell elements
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.
9

MESH QUALITY
Elements before mapping Elements after mapping
10

MESH QUALITY aspect ratio angular distortion ( skew ) angular distortion ( taper ) curvature distortion midsize node position warpage
11

MESH QUALITY
Element distortion: aspect ratio
Element distortion: warping
12

MESH QUALITY
Element distortion: tangent edges
13

MESH ADEQUACY
This stress distribution need to be modeled
This is what is modeled with one layer of first order elements
14

MESH ADEQUACY cantilever beam, model 1 terribly bad cantilever beam, model 2 also terribly bad cantilever beam model 3 a good beginning !
cantilever beam, model 4 an acceptable model cantilever beam size: modulus of elasticity: load: beam theory maximal deflection: beam theory maximal stress:
10" x 1" x 0.1"
30,000,000 PSI
150 lb.
f = 0.2"

= 90,000 PSI our definition of the discretization error :
( beam theory result - FEA result ) / beam theory result model #
1
2
3
4
FEA deflection
[in]
0.1358
0.1791
0.1950
0.1996 deflection error
[%]
32
10
2.5
0.2
FEA stress
[ PSI ]
1,500
39,713
65,275
80,687 stress error
[%]
98
56
27
10
15

MESH ADEQUACY
Two layers of second order solid elements are generally recommended for modeling bending.
Shell elements adequately model bending.
16

MESH ADEQUACY
Incorrect shell elements meshing using automatically generated mid-surface
17