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 follows:

For each face, define two diagonal vectors as

where pl1 and pl2 are the place vectors of the face treated as CQUAD4. See the definition of reference plane for quadrilateral element or face. The diagonal vectors for a planar parallelogram can be show below:

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 of each of the two opposite faces are projected onto this reference plane. The angles between the projected and the projected are computed as . The maximum of 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

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 the definition of hoe normal offset of 3-node edge.

·        Hoe Tangent Offset

The hoe tangent offset is the maximum of its edges tangent offset values. See the definition of hoe tangent offset of 3-node edge.

CHEXA 2nd-order Default Bounds

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Element Quality Check