# CTETRA Element Checks and Default Bound Values

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

- 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) $$\text{collapse}\hspace{0.17em}=\hspace{0.17em}\text{MIN}\hspace{0.17em}({\text{h}}_{\text{i}}\hspace{0.17em}/\hspace{0.17em}\text{sqrt}({\text{A}}_{\text{i}})\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\text{i}\hspace{0.17em}=\hspace{0.17em}1,2,3,4$$ - 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) $$\text{EA}\hspace{0.17em}=\hspace{0.17em}\text{MAX}\hspace{0.17em}|\hspace{0.17em}90\hspace{0.17em}-\hspace{0.17em}\text{ANGLE}({\text{N}}_{\text{ki}},\hspace{0.17em}{\text{N}}_{\text{li}})\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\text{i}\hspace{0.17em}=\hspace{0.17em}1,\hspace{0.17em}\mathrm{...},\hspace{0.17em}6$$

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

- 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
- Edge Angle
- 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.