# CTETRA Element Checks and Default Bound Values

## CTETRA 1st-order (4-noded) Element Checks

The following qualities of the CTETRA 1st-order element are checked:
Aspect Ratio
The aspect ratio of a CTETRA 1st-order element is defined as the maximum of the aspect ratio of its four triangular faces. Each face is treated as a CTRIA3 element.
Face Skew Angle
The face skew angle of a CTETRA 1st-order element is defined as the maximum of the skew angles of its four triangular faces. Each face is treated as a CTRIA3 element.
Vertex Angle
The same vertex angle check is performed for all of the faces, and each is treated as a triangular (CTRIA3) or quadrilateral (CQUAD4) element. The minimum and maximum values reported for the element.
Collapse
The collapse of a CTETRA 1st-order element is defined as the minimum of four values, each calculated as the ratio between the distance from a vertex to its opposing face, and the square root of the area of the opposing face.(1)
$\text{collapse} = \text{MIN} \left({\text{h}}_{\text{i}} / \text{sqrt}\left({\text{A}}_{\text{i}}\right) \text{i} = 1,2,3,4$
The reported value is normalized by 1.2408, which gives the equilateral tetra a collapse value of 1. As the tetra collapses, the collapse value approaches 0.
Edge Angle
An edge angle is the absolute value of the angle between two faces sharing a common edge subtracted from 90 degrees. The edge angle (EA) of a CTETRA 1st-order element is defined as the maximum of its six edge angles.(2)
$\text{EA} = \text{MAX} | 90 - \text{ANGLE}\left({\text{N}}_{\text{ki}}, {\text{N}}_{\text{li}}\right) \text{i} = 1, ..., 6$
Where, Nki and Nli are the normal vectors of faces k and l that have a common edge i.

## CTETRA 2nd-order (10-noded) Element Checks

The following qualities of the CTETRA 2nd-order element are checked:
Aspect Ratio
This quality is calculated using only the corner nodes. Its definition is the same as that used for the CTETRA 1st-order element.
Face Skew Angle
This quality is calculated using only the corner nodes. Its definition is the same as that used for the CTETRA 1st-order element.
Vertex Angle
This quality is calculated using only the corner nodes. Its definition is the same as that used for the CTETRA 1st-order element.
Collapse
This quality is calculated using only the corner nodes. Its definition is the same as that used for the CTETRA 1st-order element.
Edge Angle
This quality is calculated using only the corner nodes. Its definition is the same as that used for the CTETRA 1st-order element.
Hoe Normal Offset
The hoe normal and tangent offsets of the CTETRA 2nd-order element are defined as the maximum of the hoe normal and tangent offsets of its 6 edges, respectively. See Hoe Normal Offset of 3-Node Edge
Hoe Tangent Offset
The hoe normal and tangent offsets of the CTETRA 2nd-order element are defined as the maximum of the hoe normal and tangent offsets of its 6 edges, respectively. See Hoe Tangent Offset of 3-Node Edge

## CTETRA Default Bounds

Information Default values for warning message Default values for error message Default values for validity check
Lower Limit Upper Limit Lower Limit Upper Limit Lower Limit Upper Limit
Aspect Ratio - 100.0 - 1000.0 - 1.0E5
Face Skew Angle - 75.0 - 85.0 - 90.0
Collapse 0.001 100.0 0.0 100.0 0.0 1000.0
Edge Angle (CTETRA4) - 75.0 - 87.0 - 90.0
Edge Angle (CTETRA10) - 75.0 - 90.0 - 90.0
Hoe Normal Offset - 0.30 - 0.60 - 1.0E5
Hoe Tangent Offset - 0.20 - 0.25 - 0.50

The values used for warning and error checks may be adjusted by the ELEMQUAL Bulk Data Entry, but validity checks are hard-coded.