Element Quality Calculation: I-DEAS

Additional element checks not listed here are not part of the solver’s normal set of checks, and therefore use HyperMesh check methods.

Checks used for both 2D and 3D elements

These checks apply to both types of elements, but when applied to 3D elements they are generally applied to each face of the element. The value of the worst face is reported as the 3D element’s overall quality value.

Check

Description

Stretch (Aspect Ratio)

Stretch is evaluated differently depending on whether the element is triangular or quadrilateral:

•	For trias: the radius of the largest circle that fits within the element is divided by the longest edge, then multiplied by the square root of 12.

ideas_stretch_tria

•	For quads: the minimum edge length is divided by the maximum diagonal length. The result is multiplied by the square root of 2.

Note:

The inverse of stretch displays on-screen in HyperMesh as the aspect.

Chordal Deviation

Chordal deviation of an element is calculated as the largest distance between the centers of element edges and the associated surface. 2nd order elements return the same chordal deviation as 1st order, when the corner nodes are used due to the expensive nature of the calculations.

chordal_deviation

Jacobian

This measures the deviation of an element from its ideal or "perfect" shape, such as a triangle’s deviation from equilateral. The Jacobian value ranges from 0.0 to 1.0, where 1.0 represents a perfectly shaped element. The determinant of the Jacobian relates the local stretching of the parametric space which is required to fit it onto the global coordinate space.

HyperMesh evaluates the determinant of the Jacobian matrix at each of the element’s integration points (also called Gauss points) or at the element’s corner nodes, and reports the ratio between the smallest and the largest. In the case of Jacobian evaluation at the Gauss points, values of 0.7 and above are generally acceptable. You can select which method of evaluation to use (Gauss point or corner node) from the Check Element Settings window.

Length (min.)

Minimum element lengths are calculated using one of two methods:

•	The shortest edge of the element. This method is used for non-tetrahedral 3D elements.

•	The shortest distance from a corner node to its opposing edge (or face, in the case of tetra elements); referred to as "minimal normalized height".

height2closenode

Skew

This check measures the deviation of an element’s corners from 90 degrees (for quads) or 60 degrees (for trias). The check calculates skew by finding:

for quadrilaterals, or

for triangular elements

Where alpha is the angle of each corner. An ideal/equilateral element has a skew of zero, as none of its corners deviate from the target (90 or 60 degrees).

Taper

Taper ratio for the quadrilateral element is defined by first finding the area of the triangle formed at each corner grid point:

HM_taper

These areas are then compared to one half of the area of the quadrilateral.

HyperMesh then finds the smallest ratio of each of these triangular areas to ½ the quad element’s total area (in the diagram above, "a" is smallest). The resulting value is subtracted from 1, and the result reported as the element taper. This means that as the taper approaches 0, the shape approaches a rectangle.

ideas_taper

Triangles are assigned a value of 0, in order to prevent HyperMesh from mistaking them for highly-tapered quadrilaterals and reporting them as "failed".

Warpage

The amount by which an element (or in the case of solid elements, an element face) deviates from being planar. Since three points define a plane, this check only applies to quads. The quad is divided into two trias along its diagonal, and the angle between the trias’ normals is measured.

Checks Used Only for 3D Elements

The following check only applies to 3D elements.

Stretch (volume aspect ratio)

Stretch is evaluated differently depending on whether the element is a tetrahedron, Wedge, Brick, or Pyramid:

•	For tetras: the radius of the largest sphere that fits within the element is divided by the longest edge. This value is then multiplied by the square root of 24.

•	For wedges: each face is evaluated for its 2D stretch, and the worst value is reported. This means that the value reported for vol AR should always be the same as that reported for aspect.

•	For bricks: the minimum edge length is divided by the maximum diagonal length. The result is multiplied by the square root of 3.

•	For pyramids: no check is defined, so HyperMesh performs its standard check in which each face is evaluated as a 2D object and the worst result reported.