References for mesh quality considerations
 

Hey!

I am looking for some good references (books, journals, experiences etc. ) to study the effects of the FEM mesh quality. I would like to see results and comparison of situations e.g. for the following things which one may encounter while meshing:

-corner radius vs. sharp edge mesh or modeled corner
-hole radius vs. when to neglect the hole
-aspect ratio vs. quality
-skewnes vs. quality
-shell element vs. solid elements in different loading conditions
-general mesh size and side length ratio

-element shape: Math people seem to like triangles while structural engineers prefer quadrilateral elements? What are the benefits and disadvantages of both of these?

I know that many of these things depend on the case, material etc. but some kind of base must exist.

I have been doing CFD in the past but now I need to extend my skills to FEM world and the first thing weird here is the meshing.



Cheers

I work in the space industry doing FEM analyses on satellites but I come from a CFD background.

The first thing you will have noticed is how low quality and coarse all of the FEM meshes are! I can't give you academic references but I can give you some 'industry background'.

How to know when your mesh is fine enough: In my experience in CFD, you will run a few meshes of different fineness and compare results. In FEM, it is possible to play with the post-processing options. For example, element stresses can calculated from the nodal displacements in several different ways (e.g one value in the 'centre' of the element using a bilnear interpolation of the 4 nodal values, or the 'corner' method which gives 4 values per element (one stress value per node with the interpolation being done from the closest nodes on adjacent elements in the case of an all quad mesh). You then have different options to do with taking the average, or the maximum of these values. If the average/max values do not change too much (5% maybe, but there is no rule) then your element can be considered fine enough. If they do change too much, then the stresses change too much over one element and your mesh is too coarse.

Treatment of holes: Once you have decided that your mesh is generally fine enough, you have two main choices:

1) If your circle diameter is around the size of an element, mesh your circular hole as a rectangle (simply delete an element to make your hole) and apply a Kt (concentration factor) to the stresses on the corners of your hole. For a circle Kt=3, for other shapes it can be as much as 7 or 8 depending on radius of curvature etc.

2) If possible, refine your mesh around the hole. As a rough guide, for a radius of 15-50mm, you will want to have 1 element per mm along the edge, with high quality quad elements on the edge.

In my experience, the sharp edge hole with Kt tends to over-estimate the stresses by about 30% for basic static analyses. In part this is because the Kt I take (pessimistic case) assumes purely axial loading, although Kts for bi-axial loads are available.


Quad vs Triangular elements: Triangular elements are around 5% 'stiffer' than quads so it's preferable to not to have too many if you want a pessimistic result for the first natural frequency of your structure (in the space industry where we strive to have everything as pessimistic as possible so that we are sure it works). There are obviously different considerations analyses where the stresses and displacements are more important rather than frequencies.