# CHEXA Element Checks and Default Bound Values

## CHEXA 1st-order (8-noded) Element Checks

The following qualities of the CHEXA 1st-order element are checked:
Aspect Ratio
The aspect ratio of a CHEXA 1st-order element is defined as the maximum aspect ratio among its six faces; each treated as a CQUAD4 element.
Face Skew Angle
The face skew angle of a CHEXA 1st-order element is defined as the maximum skew angle among its six faces; each treated as a CQUAD4 element.
Vertex Angle
The same vertex angle check is performed for all of the faces, and each is treated as a quadrilateral (CQUAD4) element. The minimum and maximum values reported for the element.
Face Warpage
The face warpage of a CHEXA 1st-order element is defined as the maximum warpage among its six faces; each treated as a CQUAD4 element.
Twist Angle
The twist angle of a CHEXA 1st-order element is defined as the maximum rotation of one face with respect to its opposite face. The calculation is done as:
For each face, define two diagonal vectors as:
$\begin{array}{l}{D}_{1}=0.25\left(P{L}_{1}+P{L}_{2}\right)\\ {D}_{2}=0.25\left(P{L}_{1}-P{L}_{2}\right)\end{array}$
Where, $P{L}_{1}$ and $P{L}_{2}$ are the place vectors of the face treated as CQUAD4. See Reference Plane for Quadrilateral Element or Face.
Then, for each pair of opposing faces, a reference plane that is perpendicular to the axis connecting the centroids of the faces is constructed. The diagonal vectors ${D}_{1}$ and ${D}_{2}$ of each of the two opposite faces are projected onto this reference plane. The angles between the projected ${D}_{1}$ and the projected ${D}_{2}$ are computed as ${t}_{1}$ and ${t}_{2}$ . The maximum of ${t}_{1}$ and ${t}_{2}$ is defined as the relative rotation between these two opposite faces (TAF). Finally, the twist angle (TA) of a CHEXA 1st-order is calculated as the maximum relative rotation of its three pairs of opposing faces.
Edge Angle
An edge angle is the absolute value of the angle between two faces sharing a common edge, subtracted from 90 degrees. For warped faces, the projected planes are used to compute the face normals used for the angle calculation. The edge angle of a CHEXA 1st-order is defined as the maximum edge angle in the element.

## CHEXA 1st-order 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 - 60.0 - 75.0 - 90.0
Face Warp Angle - 30.0 - 60.0 - 180.0
Twist Angle - 30.0 - 90.0 - 180.0
Edge Angle - 60.0 - 85.0 - 90.0

## CHEXA 2nd-order (20-noded) Element Checks

The following qualities of the CHEXA 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 CHEXA 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 CHEXA 1st-order element.
Vertex Angle
This quality is calculated using only the corner nodes. Its definition is the same as that used for the CHEXA 1st-order element.
Face Warpage
This quality is calculated using only the corner nodes. Its definition is the same as that used for the CHEXA 1st-order element.
Twist Angle
This quality is calculated using only the corner nodes. Its definition is the same as that used for the CHEXA 1st-order element.
Edge Angle
This quality is calculated using only the corner nodes. Its definition is the same as that used for the CHEXA 1st-order element.
Hoe Normal Offset
The hoe normal offset is the maximum of its edges normal offset values. See Hoe Normal Offset of 3-Node Edge
Hoe Tangent Offset
The hoe tangent offset is the maximum of its edges tangent offset values. See Hoe Tangent Offset of 3-Node Edge

## CHEXA 2nd-order 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 - 60.0 - 75.0 - 90.0
Face Warp Angle - 30.0 - 60.0 - 180.0
Twist Angle - 30.0 - 75.0 - 180.0
Edge Angle - 60.0 - 89.0 - 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.