The Aspect Ratio
- quality criterion for mesh elements is defined as follows: The Aspect Ratio
- quality criterion for mesh elements is defined as follows:
- -
For a triangle - 2D element consisting of 3 nodes a the Aspect - Ratio is calculated as the ratio of the length, h2, of the edge - of this triangle, to the height, h1. The ratio of h2 to h1 is then multiplied - by 3(1/2) /2, so that - a “perfect” element in the shape of an equilateral triangle will be equal - to 1. This procedure is repeated for the remaining two edges of the triangle, - and the largest value is retained as the Aspect - Ratio for the element.
- -
- -
- -
For a quadrangle - 2D element consisting of 4 nodes the - Aspect Ratio is the ratio of the - element's longest side to its shortest side.
- -
To apply the Aspect Ratio quality criterion to your mesh:
- -- -
1. Display your mesh in the viewer.
- -- -
2. Choose Quality
- Controls > Aspect Ratio or click 
button in the
- toolbar. Your mesh will be displayed in the viewer with its elements colored
- according to the applied mesh quality control criterion:
- -
The Aspect Ratio
+ quality criterion for mesh elements reveals the degree of conformity of
+ a mesh element to the regular element of its type (with all edges having
+ the same length). The
+ criterion can be defined as
where К
+ is the considered element of the mesh, hmax is the diameter of the element
+ К (i.e. the length of the longest edge), рк is the radius of the sphere
+ inscribed in the element K, and a
+ is a normalisation value chosen so that QK = 1 when К is an equilateral
+ simplex.
+ +
The value of QK varies between 1 and +oo and the + closer it is to 1, the better the element К is.
+ +The Aspect Ratio + of a triangle 2D element consisting + of 3 nodes is calculated by the formula:
+ +
,
+ +
where рк is the half perimeter of the + element K and SK is its surface.
+ ++ +
+ +
The Aspect + Ratio of a quadrangle 2D + element consisting of 4 nodes is the worst (i.e. the greatest) value from + all triangles which can be built taking three nodes of the quadrangle. + There are four triangles to consider:
Note, that the Aspect Ratio criterion is + applicable to 2D mesh elements only. For 3D elements we use the Aspect + Ratio 3D criterion.
+ ++ +
To apply the Aspect Ratio quality criterion to your mesh:
+ ++ +
1. Display your mesh in the viewer.
+ ++ +
2. Choose Controls
+ > Aspect Ratio or click button in the toolbar.
+ Your mesh will be displayed in the viewer with its elements colored according
+ to the applied mesh quality control criterion:
+ +
+ +
See Also + a sample TUI Script of an Aspect + Ratio quality control operation.
+ ++ + + +