Mesh Quality Checks
The quality of mesh 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, numerical accuracy is best achieved by
a mesh with uniform perfect tetrahedral elements whose edges are equal
in length. For a general geometry, it is not possible to 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
some of their edges much longer than others. When the edges of an element
become much different in length, the accuracy of the results deteriorates.
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 defined as 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 aspect ratio
check is automatically used by the program to check the quality of the
mesh.
Jacobian Points.
Parabolic elements can map curved geometry much more accurately than linear
elements of the same size. The mid-side nodes of the boundary edges of
an element are placed on the actual geometry of the model. In extremely
sharp or curved boundaries, placing the mid-side nodes on the actual geometry
can result in generating distorted elements with edges crossing over each
other. The Jacobian of an extremely distorted element becomes negative.
An element with a negative Jacobian causes the analysis program to stop.
The Jacobian check is based on a number of
points located within each element. The software gives you a choice to
base the Jacobian check on 4,
16, 29
Gaussian points or At Nodes.
It is recommended to 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 mid-side 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
it is generally seen that a Jacobian Ratio of forty or less is acceptable.
The software adjusts the locations of the mid-side nodes of distorted
elements automatically to make sure that all elements pass the Jacobian
check.
For high order shells, the
Jacobian check uses 6 points located
at the nodes.
To set the Jacobian check options for a study:
In the Simulation study tree, right-click the
Mesh icon and select Create.
Expand Advanced.
Specify the number
of points for Jacobian points.
Under Options,
select Save settings without meshing
to save the options without meshing or click to save the
options and mesh the model.