HyperMesh and BatchMesher

Element Quality Calculation: Patran

Element Quality Calculation: Patran

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Element Quality Calculation: Patran

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

 

Checks used for both 2D and 3D elements

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.

Check

Description

Aspect Ratio (triangle)

For triangles, the length of a side is divided by the height of the triangle from that side to its opposite node, then multiplied by ½ of the square root of 3.  In a perfect equilateral triangle, this formula produces a value of 1.  The process is performed for each of the three sides, and the largest value of the three is reported as the aspect ratio.

patran_aspect_ratio_tria      

patran_aspect

Aspect Ratio (quad)

If the element is not flat, it is 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.

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

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 1 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

Skew (triangle)

Patran evaluates triangular skew by constructing a line from one of the triangle’s nodes to the midpoint of its opposite side, and another line connecting the midpoints of the remaining two sides.

patran_skew_tria

An angle between these created lines is compared to 90 degrees to find its deviation from square.  This process is then repeated for each of the remaining two nodes, and the largest of the three computed angle deviations is reported as the element’s skew.

Skew (Quad)

The skew test begins by bisecting the four element edges. This creates an origin at the vector average of the four corners, with the x-axis extending from the origin to the bisector on edge 2. Next, finding the cross-product of the x-axis and the vector that stretches from the origin to the midpoint of edge 3 defines the z-axis. With the x and z axes defined, their cross-product defines the y-axis.

patran_skew_quad

Finally, subtracting the angle α (located between the y axis and the line bisecting edges 1 and 3) from 90 degrees reveals the element skew.

Taper

Patran calculates taper by first averaging the corner nodes to find the element center, and creating lines between this center and the corner nodes to split the element into four triangles.

patran_taper

The taper calculation is simply the smallest triangle’s area divided by the average of all the triangle areas—or, put another way, the taper is quadruple the area of the smallest triangle, divided by the sum of the areas of all four triangles:

patran_taper_equation

Note:For the sake of display compatibility, HyperMesh reports an equivalent value for Taper.  Taper is determined as above, but is then subtracted from 1 to produce a number between zero and one.  Thus, as the element taper decreases, the reported value approaches zero (a perfect square).  Triangles are assigned a value of zero to prevent them from showing up as failed quads.

Warpage

The warpage test bisects the element edges, creating a point at the vector average of the element corners. This point serves as the base node for a plane, with the plane’s x-axis extending from the base node to the bisector on edge 2 of the element. The plane normal (z-axis) is in the direction of the cross-product of this x-axis and the vector from the origin to the bisector of edge 3. Each corner of the quad is then the same distance, h, from the plane.

patran_warpage

Next, Patran measures the length of each half-edge, and calculates the arcsine of the ratio of h to the shortest half-edge length (L):

patran_warpage_equation

 

Checks Used Only for 3D Elements

The following checks only apply to 3D elements.

Check

Description

Vol. Aspect Ratio (Tetrahedron)

Patran finds the aspect ratio of Tetra elements by finding the ratio between a vertex height and ½ the area of the opposing face.  This process is repeated for each vertex, and the largest ratio found.

patran_volar_tet

Next, Patran multiplies the largest ratio found by 0.805927 (the corresponding ratio of an equilateral tetrahedron). The result is reported as the element’s aspect ratio, with a value of 1 representing a perfect equilateral tetrahedron.

Vol. Aspect Ratio (pyramid)

The Aspect Ratio of a pyramid element is simply the ratio of the element’s longest edge length to its shortest edge length.

Vol. Aspect Ratio (wedge)

This test begins by averaging the triangular faces of the element to create a triangular mid-surface.  Next, it finds the aspect ratio of the mid-surface (as for a tria element).  Then it compares the average height (h1) of the wedge element to the mid-surface’s maximum edge length (h2).

patran_volar_wedge

If the wedge height h1 exceeds the edge length h2, the wedge’s aspect ratio equals the mid-surface aspect ratio multiplied by h2, then divided by the average distance between the triangular faces (h3).

If the wedge height h1 is less than the edge length h2, the wedge aspect ratio equals either the mid-surface aspect ratio, or the maximum edge length h2 divided by the average distance between the triangular faces (h3), whichever is greater.

patran_vol_aspect

Vol. Aspect Ratio (hexahedron)

Each face of the hex element is treated as a warped quadrilateral, and its center point found. The volume aspect ratio is simply the ratio of the largest distance h between the center points of any two opposing faces, to the smallest such distance:

patran_volar_hex

patran_vol_aspect_02

 

 

See Also:

How Element Quality is Calculated

Element Quality Calculation: HyperMesh