Warping Factor

Warping factor is computed and tested for some quadrilateral shell elements, and the quadrilateral faces of bricks, wedges, and pyramids. A high factor may indicate a condition the underlying element formulation cannot handle well, or may simply hint at a mesh generation flaw.

It is defined as the angle between the normals to two planes formed by splitting the quad element along the diagonals.  The maximum angle of the two possible angles is reported as the warp angle.

Jacobean Ration

Jacobian ratio is computed and tested for all elements except triangles and tetrahedra that (a) are linear (have no midside nodes) or (b) have perfectly centered midside nodes. A high ratio indicates that the mapping between element space and real space is becoming computationally unreliable.

The jacobian is a scale factor arising because of the transformation of the coordinate system.   Elements are tansformed from the global coordinates to local coordinates (defined at the centroid of every element), for faster analysis times.

Aspect Ratio

2-D:

Length / height ratio: δx/ δy

3-D

Area ratio: Radius ratio of circumscribed / inscribed circle

Element Quality

This metric is based on the ratio of the volume to the sum of the square of the edge lengths for 2D quad/tri elements, or the square root of the cube of the sum of the square of the edge lengths for 3D elements. 

This can also be expressed as follows:
• For two-dimensional quad/tri elements:

• For three-dimensional brick elements:

The following table lists the value of C for each type of element:

• The Element Quality option provides a composite quality metric that ranges between 0 and 1. 
• A value of 1 indicates a perfect cube or square while a value of 0 indicates that element has a zero or negative volume.