# Mesh Quality Checks

Mesh quality plays a key role in the accuracy of the results. SOLIDWORKS Simulation uses the following parameters to measure the quality of elements in a mesh.

## Aspect Ratio

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.

Because of 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

A good-quality mesh has an Aspect ratio less than 5 for most of its elements (90% and above). Create a Mesh Quality Plot to plot the Aspect ratio of all elements.

## Jacobian Ratio

Available for second order mesh elements (high quality solid and shell mesh).

The Jacobian ratio measures the deviation of an element’s shape from an ideally shaped element (one that has straight edges with equal lengths). The Jacobian ratio of a perfect second order tetrahedral element with linear edges is 1.0. The Jacobian ratio of an element increases as the curvature of the element edges increases to map a curved geometry.

Near extremely sharp or curved boundaries, the edges of an element can cross over each other and the element becomes distorted, resulting in self-intersecting geometry. Distorted elements have a negative Jacobian ratio and produce inaccurate results.

In the Mesh PropertyManager, the Issue warning for distorted elements option alerts you if there are distorted elements in the mesh. To remove distorted elements, first check the model for any geometry irregularities. Refine the mesh in areas where distorted elements exist.

The Jacobian ratio check considers the Gaussian points located within each element. The default value in a new study is 16 Gaussian points.

Recommendation: Set Jacobian check to At Nodes when using the p-method to solve static problems.
For high-order shells, the Jacobian check uses 6 points located at the nodes.

A good quality mesh has a Jacobian ratio between 1 and 10 for the majority of its elements (90% and above). Create a Mesh Quality Plot to plot the Jacobian ratio of all elements.

For most models, elements at regions of high curvatures have higher Aspect and Jacobian ratios. If the elements with the highest Aspect and Jacobian ratios (larger than 10) are away from critical areas for the analysis, it might not be worthwhile to refine the mesh in these areas. However, for areas that are critical for the simulation, you can refine the mesh locally to reduce the Aspect and Jacobian ratios for the poor quality elements and improve the simulation results.

Depending on the geometry of the model, subsequent levels of mesh refinement might not improve further the mesh quality and the simulation results. After each level of mesh refinement, confirm that the mesh quality plots for Aspect ratio and Jacobian ratio show fewer poor-quality elements. In addition, ensure that after each successful mesh refinement, the simulation results converge to finite values.

## Element Area

(Available only for shell mesh).

The Element area check measures the surface area of each element against a limit surface area value. The mesh algorithm identifies elements with surface areas less than the limit value as poor-quality elements and removes these elements from the mesh. The table lists the accepted limit values of an element's surface area for each mesher.
Mesher Limit of Element Area
Standard (Mesh element tolerance) ^2 * 0.001
Curvature-based (Minimum element size) ^2 * 0.001
Blended Curvature-based (Minimum element size) ^2 * 0.001

To view a Mesh Quality Diagnostics plot based on the Element area:

In the Mesh Quality Diagnostics PropertyManager, under Display, select Element area.

## Skewness

(Available only for shell mesh.)

Skewness is the angular measure of an element’s quality with respect to the angles of an ideal element type. For a triangular element, the skewness is the ratio of the angular deviation from an element that has an ideal shape.

= largest angle of element face

= smallest angle of element face

= angle of an equiangular element (equals 60° for an equilateral triangle and 90° for a square)

A perfect equiangular triangle has a skewness value of 0. SOLIDWORKS Simulation identifies elements that have skewness values greater than 0.9 as poor-quality elements. You can specify a skewness value as less than 0.9 to apply a stricter criterion.

To view a Mesh Quality Diagnostics plot based on the Skewness:

In the Mesh Quality Diagnostics PropertyManager, under Display, select Skewness.