The Quality Tests

• Angles
  Two angle tests are available; maximum angle (`MAXANG') and minimum angle (`MINANG'). The corner angles on each face of 2D and 3D elements are checked. For higher order elements the lines connecting the corner to midside nodes are used rather than corner to corner nodes.

  The definition of an ideal angle is dependant on the element type, for example an ideal QU4 should have 4 angles of 90 degrees whereas an ideal TR6 should have 3 angles of 60 degrees.

• Aspect Ratio
  The aspect ratio test (`ASPECT') measures the elongation of the element. It is calculated as the ratio of the length of the smallest side of the element to the length of the longest. Aspect ratio varies from 1 for an ideal QU4 to 0 for a degenerate element.
• Midside Node Position
  One parameter regularly examined in higher order elements, especially in cases of expected high stress gradient, is the position of the midside node relative to the line connecting the 2 corner nodes.

  Two tests are available. Firstly, an offset test (`NODOFF') which calculates the ratio of the lengths of the projected line connecting the corner node and the midside node, and the line connecting the corner node to the point midway between the 2 corner nodes. The ideal offset is zero.

  Secondly, a bulge test (`BULGE') which calculates the ratio of the perpendicular distance from the midside node to this line and the length of the line is called the `BULGE'. The ideal bulge is zero.

• Warp
  An out of plane test (`WARP') measures the extent to which a corner node lies out of plane and is calculated only for elements with 4 noded faces. A neutral plane is defined positioned at the element centroid perpendicular to the surface normal. The deviation from each node to this surface is generated from the projection onto the surface normal of the vector joining the node to the element centroid.

  Warp is the difference between the minimum and maximum projections over the 4 nodes (the extent of warpage) divided by the square root of the length of the surface normal (calculated using the cross product).

• Jacobian
  The Jacobian test is used to detect elements with negative volumes, this is applied by default to all non-tetrahedral solid elements. Failure, which is indicated by a value of -1, can usually be remedied by using GEOMETRY FLIP on some of the body's surfaces.
• RADRAT
  RADRAT is a test for tetrahedral elements which measures the ratio of the radius of the element's insphere to the longest edge of the element. An ideally shaped element will give a value of 1.0. By default, values greater than 5.0 indicate failure. The test works from the element vertex locations only, consequently TE10 elements with poorly positioned mid side nodes may not be detected, although they may fail the alternative angle tests. (This test comes from, and is used in, the process of tetrahedral mesh generation.)

Element Angle Angle Aspect Mid-node Mid-node Warp Jacobian Radrat

Type Min Max Ratio Offset Bulge

BE2 - - - - - -

BE3 - - - .1 .1 - - -

BE4 - - - .1 .1 - - -

BE5 - - - .1 .1 - - -

TR3 25 150 .12 - - - - -

TR6 20 150 .12 .1 .1 - - -

TR9 20 150 .12 .1 .1 - - -

TR15 20 150 .12 .1 .1 - - -

QU4 40 140 .12 - - .1 - -

QU8 35 145 .12 .1 .1 - - -

QU9 35 145 .12 .1 .1 - - -

QU12 35 145 .12 .1 .1 - - -

TE4 20 160 .12 - - - - 5

TE10 20 160 .12 .1 .1 - - 5

TE16 20 160 .12 .1 .1 - - 5

PE6 30 150 .12 - - .1 0 -

PE15 30 150 .12 .1 .1 - 0 -

PE24 30 150 .12 .1 .1 - 0 -

HE8 40 140 .12 - - .1 0 -

HE16 40 150 .12 .1 .1 - 0 -

HE20 35 145 .12 .1 .1 - 0 -

HE27 35 145 .12 .1 .1 - 0 -

HE32 35 145 .12 .1 .1 - 0 -