Cubit
15.3 User
Documentation
Cubit
15.3 User
Documentation
The metrics used for hexahedral elements in CUBIT are summarized in the following table:
Function Name
|
Dimension
|
Full Range
|
Acceptable Range
|
Reference
|
Aspect Ratio
|
L^0
|
1 to inf
|
1 to 4
|
1
|
Skew
|
L^0
|
0 to 1
|
0 to 0.5
|
1
|
Taper
|
L^0
|
0 to +inf
|
0 to 0.4
|
1
|
Element Volume
|
L^3
|
-inf to inf
|
None
|
1
|
Stretch
|
L^0
|
0 to 1
|
0.25 to 1
|
2
|
Diagonal Ratio
|
L^0
|
0 to 1
|
0.65 to 1
|
3
|
Dimension
|
L^1
|
0 to inf
|
None
|
1
|
Condition No.
|
L^0
|
1 to inf
|
1 to 8
|
5
|
Jacobian
|
L^3
|
-inf to inf
|
None
|
5
|
Scaled Jacobian
|
L^0
|
-1 to +1
|
0.5 to 1
|
5
|
Shear
|
L^0
|
0 to 1
|
0.3 to 1
|
5
|
Shape
|
L^0
|
0 to 1
|
0.3 to 1
|
5
|
Relative Size
|
L^0
|
0 to 1
|
0.5 to 1
|
5
|
Shear & Size
|
L^0
|
0 to 1
|
0.2 to 1
|
5
|
Shape & Size
|
L^0
|
0 to 1
|
0.2 to 1
|
5
|
Distortion
|
L^0
|
0 to 1
|
0.6 to 1
|
6
|
With a few exceptions, as noted below, Cubit supports quality metric calculations for linear hexahedral elements only. When calculating quality metrics, that only support linear elements, for a higher order hexahedral element, Cubit will only use the corner nodes of the element.
Aspect Ratio: Maximum edge length ratios at hex center.
Skew: Maximum |cos A| where A is the angle between edges at hex center.
Taper: Maximum ratio of lengths derived from opposite edges.
Element Volume: Jacobian at hex center.
Stretch: Sqrt(3) * minimum edge length / maximum diagonal length.
Diagonal Ratio: Minimum diagonal length / maximum diagonal length.
Dimension: Pronto-specific characteristic length for stable time step calculation. Char_length = Volume / 2 grad Volume.
Condition No. Maximum condition number of the Jacobian matrix at 8 corners.
Jacobian: Minimum pointwise volume of local map at 8 corners at center of hex. Cubit also supports Jacobian calculations for hex27 elements.
Scaled Jacobian: For linear elements the minimum Jacobian divided by the lengths of the 3 edge vectors.
Shear: 3/Mean Ratio of Jacobian Skew Matrix
Shape: 3/Mean Ratio of weighted Jacobian Matrix
Relative Size: Min(J, 1/J), where J is the determinant of weighted Jacobian matrix
Shear & Size: Product of Shear and Size Metrics
Shape & Size: Product of Shape and Size Metrics
Distortion: {min(|J|)/actual volume}*parent volume, parent volume = 8 for hex. Cubit also supports Distortion calculations for hex20 elements.