Coreform Cubit 2024.8 User Documentation
The metrics used for triangular elements in Coreform Cubit are summarized in the following table:
|
Function Name
|
Dimension
|
Full Range
|
Acceptable Range
|
Reference
|
| Maximum Angle |
degrees
|
60 to 180
|
60 to 90
|
1
|
| Minimum Angle |
degrees
|
0 to 60
|
30 to 60
|
1
|
| Aspect Ratio |
L^0
|
1 to inf
|
1 to 3
|
|
| Aspect Ratio Alpha |
L^0
|
1 to inf
|
1 to 3
|
|
| Condition No |
L^0
|
1 to inf
|
1 to 1.3
|
2
|
| Deviation |
L^2
|
0 to inf
|
None
|
|
| Scaled Jacobian |
L^0
|
-1 to 1
|
0.2 to 1
|
2
|
| Relative Size |
L^0
|
0 to 1
|
0.25 to 1
|
3
|
| Shape |
L^0
|
0 to 1
|
0.25 to 1
|
3
|
| Shape and Size |
L^0
|
0 to 1
|
0.25 to 1
|
3
|
| High Order Metrics | ||||
| Distortion |
L^2
|
-1 to 1
|
0.6 to 1
|
4
|
|
Element Area
|
L^2
|
0 to inf
|
None
|
1
|
| Normalized Inradius |
L^2
|
0 to 1
|
None
|
Maximum Angle: Maximum included angle in triangle
Minimum Angle: Minimum included angle in triangle
Aspect Ratio: Ratio of circumcirle to inradius
Aspect Ratio Alpha: Ratio of longest edge length to inradius
Condition No. Condition number of the Jacobian matrix
Deviation: Absolute distance from triangle centroid to associated surface
Scaled Jacobian: Minimum Jacobian divided by the lengths of 2 edge vectors
Relative Size: Min( J, 1/J ), where J is determinant of weighted Jacobian matrix
Shape: 2/Condition number of weighted Jacobian matrix
Shape & Size: Product of Shape and Relative Size
Distortion: {min(|J|)/actual area}*parent area, parent area = 1/2 for triangular element
Element Area: (1/2) * Jacobian at corner node
Normalized Inradius: 4.0 * minimum_subtri_inradius / radius of circle containing three corner nodes
Relative Size, Shape, and Shape & Size are algebraic metrics, which have well behaved properties. Coreform Cubit encourages the use of these metrics over other metrics. These metrics are referenced to an ideal element which, in the case of triangular elements, is an equilateral triangle. Thus deviations from an equilateral triangle are measured in various ways by the algebraic metrics.
Relative size measures the size of the element vs. the size of reference element. If the element is twice or one-half the size of the reference element, the relative size is one-half. By default, the size of the reference element is the average size of all the elements that the quality command is currently evaluating.
The shape and size metric measures how both the shape and relative size of the element deviate from that of the reference element.