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.

Skew

Nastran creates lines between the midpoints of opposite sides of the element, then measures the angles between these lines.  The angle with the greatest deviation from the ideal value is used to determine skew.

Taper

Nastran finds the taper of quadrilateral elements by treating each node as the corner of a triangle (for example using one of the quad’s diagonals as the triangle’s third leg).  The areas of each of these four "virtual" triangles are compared to one half of the total area of the quadrilateral element to produce a ratio; the largest of these ratios is then compared to the tolerance value.  A value of 1.0 is a perfect quadrilateral, and higher numbers denote greater taper.

However, for the sake of consistency within HyperMesh, an equivalent taper is reported instead.  This means that the smallest area ratio found (instead of the largest ratio) is subtracted from 1, so that 0 represents a perfect quadrilateral element instead of 1.0, and greater deviation from 0 indicates greater taper.  Triangle elements are simply assigned a value of 0 to prevent HyperMesh from incorrectly identifying them as failed (highly-tapered) quads.

Warpage

First, Nastran constructs a plane based on the mean of the quad’s four points.  This means that the corner points of a warped quad are alternately H units above and below the constructed plane.  This value is then used along with the length of the element’s diagonals in the following equation:

WC = H / 2(D1+D2)

Where WC is the Warping Coefficient, H is the "height" or distance of the nodes from the constructed plane, and D1 and D2 are the lengths of the diagonals.  Thus, a perfect quad has a WC of zero.

Vol. Aspect Ratio

Nastran evaluates Tetrahedral elements by finding the longest edge length and dividing it by the shortest height (measured from a node to its opposing face).  Other 3D elements (such as hex elements) are evaluated based on the ratio of their longest edge to their shortest edge.