FEM: Mesh quality and body simplification (Part 3) - Elements Quality

-          Have ever you asked: How to analyse the quality of elements in FEM? Which types of elements are  good or bad in FEM? In this article, we will briefly answer these questions:

                  Quality of the shape of the elements:

There are some criteria that define how good or bad is the element about its shape. Below, some of most common:

Aspect ratio: It is about the ratio between wide and height of the element, dividing the longest edge length by the shortest one. How bigger it is, worse is the element quality. The ideal aspect ratio for an element is 1.0. In critical stress regions, the elements shouldn´t have its value bigger than 10.0. For other not so important regions, elements with bigger aspect ratio can be tolerated [Autodesk].

Figure 1 - Aspect ratio for triangles and quadrilaterals elements. FONT: ANSYS.

Figure 2- Example of a triangle element with high aspect ratio in the mesh.

Jacobians Ratio: A righ ratio indicates that the element shape is becoming computationally unreliable.

Figure 3 - Jacobian examples. FONT: ANSYS

Figure 4 – Jacobian example in the mesh.

Figure 5 - Only jacobian examples after applied a filter.

Parallel derivations: For a flat retangle, the best derivation is 0.

Figure 6 - Parallel derivations examples. FONT: ANSYS

Figure 7 - Parallel derivation example in the mesh.

Warping Factor: Is the torsion of nodes, changing its plane. It could happen such for 2D as 3D elements.   

Figure 8 - Warping examples. Font: ANSYS.

Figure 9- Warping example in a mesh.

Skewness: How close to equilateral or equiangular the face or cell element is, better is the quality of it.

Figure 10 - Skewness examples. FONT: ANSYS.

Figure 11 - Skewness examples in the mesh. In red, bigger is the rate of skewness.