In this section you will learn some tips for creating a better FE mesh. But the things are really messy! When your model is quite simple, remember the following advises.
Use quadrilateral elements – in general, try to use quadrilateral elements instead of triangular elements as they give more accurate results. Remember that, the four corners of a quadrilateral element should all lie on the same plane. If this is not possible, use two triangular elements in place of each quadrilateral.
Element shape – quadrilateral elements – the greatest accuracy is achieved with a square – 1:1 element. Elements with a base/height ratio up to 1:2 give good results, but elements with a ratio of 1:5 will be unreliable. However, many FEA programs have the options, which allow you to specify maximum aspect ratio. But be careful, if you specify too low aspect ratio, the program may not be able to generate the mesh successfully at all! Many a times you will be forced to use 1:50 as lowest acceptable aspect ratio value. Yikes! If you do not specify such upper limit for aspect ratio, the program may occasionally churn out elements with aspect ratio as high as 1:1,000 even if you are using a $20,000 program! Try to use rectangular (rather than quadrilateral) shaped elements whenever possible, If not, the internal angles should not vary greatly from 90°. Angles of 30° or 150° will greatly reduce accuracy. Elements with convex angles should never be used. However, due to geometry of the model, more often than not you will have to use quadrilateral elements.
Triangular elements – equilateral triangles will produce the most accurate results. However, it is always better to avoid triangular elements.
Mesh density – the mesh density need not be constant throughout the model. The program assumes a linear result distribution through the element. If the actual result through the elements is not linear but parabolic, for example, it is obvious that there will be a decrease in the accuracy. In a fine mesh, the result diagram through any one element will always be approximately linear.
Increase the number of elements where there is a greater rate of change in the internal forces. For example; around supports (where bending moments increase sharply), openings and large concentrated loads.
elements is through the element end nodes only and so nodes located along an edge of an element between end nodes are ineffective. Use triangular or trapezoidal shaped elements to step between rough and fine quadrilateral meshes.
If you have doubts as to the accuracy of the results in a particular area of the model, rerun the problem with a finer mesh in that area and compare results. The results converge to the exact solution, as the mesh becomes more refined. Life will be much troublesome if you need to analyze complex solid models. Here you need to consider many other parameters. Most FEA programs, by default, generate ‘tetrahedral’ mesh for solids. Some programs, however, allow you to specify how you want the mesh to be generated. Figure 27-1 shows how your model looks with a tetrahedral mesh. Figure 27-2 shows same model with combination of 8-noded brick, tetrahedral, 5 or 6-noded transition elements. Some programs (e.g. Algor) offer following types of mesh generations.
Standard – used for most meshes by default. It gives you the highest quality mesh and the lowest number of elements. Standard solid meshing works from the surface inward. It will make 8-node brick elements on and near the surface of the model while making 6, 5 or 4-node transition elements in the center of the model as needed.
All 8-Node Bricks – this option should be used only for processors that accept only 8-node bricks. In many cases, these are fluid flow processors (for analysis of pipe network, this topic is not discussed in this book). This option can make 4 to 5 times the number of elements as the "Standard" option.
No Pyramids – the "No Pyramids" option builds brick meshes with 8, 6 and 4- node elements, but no 5-node pyramid elements.
Tetrahedral from Quads – the "Tetrahedral from Quads" option is for generating a tetrahedral solid mesh from a quadrilateral surface mesh.
Enhanced No Pyramids – this option makes brick meshes with predominantly 8- node elements plus 6-node and 4-node elements, but no 5-node pyramid elements.
Tetrahedral – the all-tetrahedral option is for generating a nearly equilateral tetrahedral solid mesh from an equilateral triangular surface mesh. This is the most common type of mesh for a large number of FEA programs.
Figure 27-2 shows boundary condition (fixed) and pressure load of 1000 lbf/sq.inch (I had to use FPS unit because the YOKE model file was in ‘inch’ unit.)
If you’re wondering how brick or tetrahedral elements look like, this is described in just next section.
We shall come to the same ‘yoke’ model later on, when we discuss how to interpret FEA results.
Figure 27-1
In the above figure only the mesh has been shown. The boundary condition and pressure load for this particular analysis has been shown in next figure. You may use ‘coarser’ or ‘finer’ mesh in your program. Normally, the programs create the mesh using a default mesh density. If can control the mesh size/density using a slider in the program.
You may wonder whether the result will change depending on what kind of mesh you are using. Well, not really in general. However, there are special cases, where you should use particular type of mesh for best result. See the chart in next section.
Figure 27-2
I apologize if the stuffs seem too boring!
Figure 27-3 shows Von-mises stress (described later) diagram of figure 27-1 after analyzing the model in COSMOS/Design Star.
The same model with mesh as of figure 27-2, is analyzed using Algor and shown in figure 27-4.
Figure 27-3
Figure 27-4 The stress is shown in ‘psi’ (pound/sq.inch) unit.
28. Common Finite Elements library for Linear Static and Dynamic