Mesh Quality Checks

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.


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.