Explanation Of Jacobian Ratio In ANSYS® Meshing(Illustrated Expression)

You can see the various features of your mesh structure from mesh metrics in ANSYS®. One of these features is the ‘Jacobian Ratio’ You can see the average Jacobian ratio situation of a mesh structure and in this article, we will explain:

• What is ‘Jacobian Ratio’ in ANSYS® Meshing?
• How the ’Jacobian Ratio’ can be seen in ANSYS® Meshing?

Explanation Of ‘Jacobian Ratio’ Mesh Metric In ANSYS® Meshing

To see the general Jacobian ratio situation of your mesh structure, click on ‘Mesh’ tan as shown in the green box above then select the ‘Jacobian Ratio’ as shown in the red box above inside the mesh metric.

After selecting the ‘Jacobian Ratio’ for mesh metric, you can see the minimum, maximum, average, and standard deviation value of Jacobian ratios in mesh structure elements. Also, you can see the dispersion of Jacobian ratios of mesh elements according to the number of them as a chart for different element types in ANSYS®.

The jacobian ratio is about the element mid-side nodes of mesh structures and calculated according to that parameter for different element types like below.

If an element midside nodes are at the exact middle of an edge, the Jacobian ratio for a triangle is 1. This is the best value for the Jacobian ratio for triangles. As you see above, when the Jacobian ratio for triangles increases, the midside nodes of edges are coming to the center.

The same logic is valid for quadrilateral elements in ANSYS® Meshing. The perfect Jacobian ratio status is parallelepiped geometry as you see above.

Conclusion

This can be the simplest way to explain the Jacobian ratio in mesh metric. The jacobian ratio must be close to the number of 1 for a perfect mesh structure in ANSYS®.

If you have comments or questions about ‘Jacobian Ratio in ANSYS® mesh metrics’, leave them below!

NOTE: All the screenshots and images are used in education and informative purposes. Images used courtesy of ANSYS, Inc.

Image Source: ANSYS® Meshing User’s Guide