Mesh quality plays a key role in the accuracy of the results. The software uses
two important checks to measure the quality of elements in a mesh.
Aspect Ratio Check
For a solid mesh, you achieve the best numerical accuracy with a mesh that has
uniform perfect tetrahedral elements whose edges are equal in length. For a general
geometry, you cannot create a mesh of perfect tetrahedral elements.
Due to small edges, curved geometry, thin features, and sharp corners,
some of the generated elements can have much longer edges than others. When the
edges of an element differ in length substantially, the results are less
accurate.
The aspect ratio of a perfect tetrahedral element is used as the basis for
calculating aspect ratios of other elements. The aspect ratio of an element is the
ratio between the longest edge and the shortest normal dropped from a vertex to the
opposite face, normalized with respect to a perfect tetrahedral.
By definition, the aspect ratio of a perfect tetrahedral element is
1.0. The aspect ratio check assumes straight edges connecting the four corner nodes.
The software calculates the aspect ratio to check the mesh quality.
Example
 |
 |
| Element with aspect ratio
close to 1.0 |
Element with large aspect
ratio |
Jacobian Points
Parabolic elements can map curved geometry much more accurately than
linear elements of the same size. The midside nodes of the boundary edges of an
element are placed on the actual geometry of the model.
In extremely sharp or curved boundaries, the placement of midside nodes on the
actual geometry can result in generating distorted elements with edges that cross
over each other. The Jacobian ratio of an extremely distorted element becomes
negative, causing the analysis to stop.
The Jacobian ratio check is based on a number of points located within each
element. The software gives you a choice to base the Jacobian ratio check on
4, 16, 29 Gaussian points or
At Nodes.
Recommendation: Set Jacobian
check to At Nodes when using
the p-method to solve static problems.
The Jacobian ratio of a parabolic tetrahedral element, with all
midside nodes located exactly at the middle of the straight edges, is 1.0. The
Jacobian ratio increases as the curvatures of the edges increase. The Jacobian ratio
at a point inside the element provides a measure of the degree of distortion of the
element at that location.
The software calculates the Jacobian ratio at the selected number of Gaussian
points for each tetrahedral element. Based on stochastic studies, a Jacobian ratio
less than thirty is acceptable. The software adjusts the locations of the midside
nodes of distorted elements automatically to make sure that all elements pass the
Jacobian ratio check.
For high-order shells, the Jacobian
check uses 6 points located at the nodes.