# CPENTA Element Checks and Default Bound Values

## CPENTA 1st-order (6-noded) Element Checks

The following qualities of the CPENTA 1st-order element are checked:
Aspect Ratio
The aspect ratio of a CPENTA 1st-order element is defined as the maximum of the aspect ratios of its three quadrilateral faces and two triangular faces. Each quadrilateral face is treated as a CQUAD4 element and each triangular face as a CTRIA3 element.
Face Skew Angle
The skew angle of a CPENTA 1st-order element is defined as the maximum skew angle among its three quadrilateral faces and two triangular faces. Each quadrilateral face is treated as a CQUAD4 element and each triangular face 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.
Face Warpage
The face warpage of a CPENTA 1st-order element is defined as the maximum warpage among the three quadrilateral faces, each treated as a CQUAD4 element.
Twist Angle
The twist angle is defined as the rotation of one triangular face with respect to the opposite triangular face. The rotation is computed as follows: first construct a reference plane perpendicular to the line connecting the centroids of the two triangular faces. The three edges of each triangular are then projected to this reference plane. The maximum angle between the corresponding edges of the two projected triangles is reported as the twist angle of the CPENTA 1st-order element.
Edge Angle
The edge angle is the absolute value of the angle between two faces sharing a common edge, subtracted from 90 degrees. For warped quadrilateral faces, the projected planes defined by the plane vectors are used to compute the face normals (see definition of reference plane for quadrilateral element or face), which are used in the angle calculation. The edge angle of a CPENTA 1st-order is defined as the maximum edge angles in the element.

## CPENTA 2nd-order (15-noded) Element Checks

The following qualities of the CPENTA 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 CPENTA 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 CPENTA 1st-order element.
Vertex Angle
This quality is calculated using only the corner nodes. Its definition is the same as that used for the CPENTA 1st-order element.
Face Warpage
This quality is calculated using only the corner nodes. Its definition is the same as that used for the CPENTA 1st-order element.
Twist Angle
This quality is calculated using only the corner nodes. Its definition is the same as that used for the CPENTA 1st-order element.
Edge Angle
This quality is calculated using only the corner nodes. Its definition is the same as that used for the CPENTA 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

## CPENTA 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
Skew Angle - 60.0 - 75.0 - 90.0
Face Warp Angle - 30.0 - 60.0 - 180.0
Twist Angle - 30.0 - 75.0 - 90.0
Edge Angle - 75.0 - 87.0 - 90.0
Hoe Normal Offset - 0.30 - 0.60 - 1.0E5
Hoe Tangent Offset - 0.20 - 0.25 - 0.5

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