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Description

Aspect Ratio

This is the ratio of the longest edge of an element to either its shortest edge or the shortest distance from a corner node to the opposing edge ("minimal normalized height"). HyperMesh uses the same method used for length (min) described below.

For 3D elements, each face of the element is treated as a 2D element and its aspect ratio determined. The largest aspect ratio among these faces is returned as the 3D element’s aspect ratio.

Aspect ratios should rarely exceed 5:1

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.

Interior Angles

These maximum and minimum values are evaluated independently for triangles and quadrilaterals.

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:

You can choose which method to use in the Check Element Settings window.

Minimum Length / Size

HyperMesh uses three methods to calculate the minimum element size: the shortest edge (in which the length of the shortest edge of each element is used), the minimal normalized height (which is more accurate, but more complex), and the minimal height (which is the same as minimal normalized height but without a scaling factor).

minimal normalized height (MNH) is calculated differently for different element types.

For triangular elements:

For each corner node (i) HyperMesh calculates the closest (perpendicular) distance to the ray including the opposite leg of the triangle, h(i). MNH = min(hi) * 2/sqrt(3.0). The scaling factor 2/sqrt(3.0) ensures that for equilateral triangles, the MNH is the length of the minimum side.

For quadrilateral elements:

For each corner node, HyperMesh calculates the closest (perpendicular) distances to the rays containing the legs of the quadrilateral that do not include this node. The figure above depicts these lengths as red lines. Minimal normalized height is taken to be the minimum of all eight lines and the four edge lengths (thus, the minimum of 12 possible lengths).

Skew

Skew of triangular elements is calculated by finding the minimum angle between the vector from each node to the opposing mid-side, and the vector between the two adjacent mid-sides at each node of the element.

The minimum angle found is subtracted from ninety degrees and reported as the element’s skew.

Taper

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

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.

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

This is 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.

Warpage of up to five degrees is generally acceptable.