Element Quality Calculation: ANSYS

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.

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

Check

Description

Aspect Ratio (tria)

For tria elements, a line is drawn from one node to the midpoint of the opposite edge. Next, another line is drawn between the midpoints of the remaining two sides. These lines are typically not perpendicular to each other or to any of the element edges, but provide four points (three midpoints plus the vertex).

ansys_aspect_ratio_step1

Then, a rectangle is created for each of these two lines, such that one line perpendicularly meets the midpoints of two opposing edges of the rectangle, and the remaining edges of the rectangle pass through the end points of the remaining line. This results in two rectangles, one perpendicular to each of the two lines:

ansys_aspect_ratio_step2

Third, this process is repeated for each of the remaining two nodes of the tria element, resulting in the construction of four additional rectangles (six in total).

Finally, each rectangle is examined to find the ratio of its longest side to its shortest side. Of these six values—one for each rectangle—the most extreme value is then divided by the square root of three to produce the tria aspect ratio.

The best aspect ratio (an equilateral tria) is one. Higher numbers indicate greater deviation from equilateral.

Aspect Ratio (quad)

If the element is not flat, it’s projected to a plane which is based on the average of the element’s corner normals. All subsequent calculations are based on this projected element rather than the original (curved) element.

Next, two lines are created which bisect opposite edges of the element. These lines are typically not perpendicular to each other or to any of the element edges, but they provide four midpoints.

ansys_aspect_ratio_quad_step1

Third, a rectangle is created for each line, such that the line perpendicularly bisects two opposing edges of the created rectangle, and the remaining two edges of the rectangle pass through the remaining line’s endpoints. This creates two rectangles—one perpendicular to each line.

ansys_aspect_ratio_quad_step2

Finally, the rectangles are compared to find the one with the greatest length ratio of longest side to shortest side. This value is reported as the quad’s aspect ratio. A value of one indicates a perfectly equilateral element, while higher numbers indicate increasingly greater deviation from equilateral.

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:

•	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_tet

Angle Deviation (Skew)

This check only applies to quadrilateral elements, and relies upon the angles between adjacent legs at each corner node (that is, the interior angles at each corner). Each angle is compared to a base of 90 degrees, and the one with the largest deviation from 90 is reported as the angle deviation. Triangular elements are given a value of zero.

Warping Factor

This test applies to quadrilateral elements as well as the quadrilateral faces of 3D bricks, wedges, and pyramids.

Warping Factor is calculated by creating a normal from the vector product of the element’s two diagonals. Next, the element’s area is projected to a plane through the average normal. Finally, the difference in height is measured between each node of the original element and its corresponding node on the projection. For flat elements, this is always zero, but for warped elements one or more nodes will deviate from the plane. The greater the difference, the more warped the element is.

ansys_warp_factor

The warping factor is calculated as the edge height difference divided by the square root of the projected area.

Checks Used Only for 3D Elements

ANSYS does not use any exclusively 3D checks within HyperMesh, but HyperMesh does use its own when ANSYS is set as the solver. See the topic on Element Quality Calculation: HyperMesh for details on the 3D checks.