How Do I Choose Mesh Size?

Mesh size is one of the most common problems in FEA. There is a fine line here: bigger elements give bad results, but smaller elements make computing so long you don’t get the results at all. You never really know where exactly is your mesh size on this scale. Learn how to choose the correct size of square mesh and estimate at which mesh size accuracy of the solution is acceptable.

As an example, I will use a simple discretely supported shell. As an “outcome” I will use the critical load multiplier of the first eigenvalue.

It’s perhaps worth mentioning that the “outcome” can be anything that interests you. If you want to know the certain stress component in a certain node, or a displacement of selected DOF that is ok. Whatever you choose goes, as long as it is actually influenced by the mesh size! I took the multiplier simply as it is easy to obtain, and linear buckling computes very fast.

Square Mesh

Choose a correct mesh size

You can see the model I used below. Notice how deformation shape and outcomes changes with the mesh refinement. I should write that mesh refinement check (often called mesh convergence) should be made for each problem. This is somewhat true but let’s face it, you won’t make it for each problem most likely… it simply takes a lot of time! I would suggest you do such a study for some of the most important projects/parts and based on that experience you can extrapolate the knowledge to similar problems.

Mesh size influence results from linear buckling analysis of a shell. In this example, I am using QUAD4 elements (normal 4 node quadrilateral elements, sometimes referred to as “S4”). In order to establish suitable finite element size:

Perform chosen analysis for several different mesh sizes.

Notice where high deformations or high stresses occur, perhaps it is worth to refine mesh in those regions.

Collect data from analysis of each mesh: outcome, number of nodes in the model, computing time

For our shell, I have performed some analysis for different element sizes. On the drawing above you can see the outcome for few selected meshes. Please notice, that for biggest elements actual eigenvalue shape is different than in the case of models with more refined mesh.

What mesh size is “small enough”?

Usually smaller mesh means more accurate results, but the computing time gets significant as well.

You should search for a balance between computing time and accuracy. In some instances you can increase computing time over 2 times to improve accuracy by 1% – for me, that seems unreasonable. Knowing your problem you will know best what makes sense and what doesn’t, based on what accuracy do you need.

When mesh density is being discussed in tutorials, different problems are solved with known analytical solution. You can then easily compare the FEA outcome to a known solution – you get an error value without trouble. This is a fantastic approach that can teach you a lot, but unfortunately in reality you don’t know the correct answer… so you can’t really do that can you?