FEA for beginners (Part I)
The main idea of this post is to provide an overview of the outline of a Finite Element Analysis for people who are not familiar with this engineering tool.
The starting point for every Finite Element Analysis is a real problem which has to be solved. For that purpose we have to create an idealised structure and, from that idealisation, we should be able to design a discrete model. Hence, using the Finite Element Method, a discrete solutions can be obtained for that model.
Up to this point, we should have been able to obtain an approximated solution for our problem. Now it is time to analyse the results. In these terms, we should look for obvious errors such as any inconsistency of the boundary conditions or physically impossible displacements. Then judging if those errors are acceptable or not and trying to compare them with other approaches (e.g. hand calculations) we should refine our model and repeat the process.
An important aspect to take into account when refining our model is the mesh. It is always useful to start with a coarse mesh and then perform a sensitivity analysis, paying special attention to the quality of the mesh (i.e. checking the Jacobian, aspect ratio…). In addition, the energy should also be considered, due to the fact that by studying the different energy results,as well as the distortion of the mesh, we will be able to identify a very common issue known as “hourglass”, which is a non-zero energy mode that can lead to a non-physical behaviour. Don’t worry, I will try to cover these potential problems in more detail in future posts.
In order to illustrate these ideas, some basic steps are introduced below. Hopefully you will find these steps useful for creating a reliable methodology for your analyses.
- Understand the real problem. Try to fully understand what the requirements are and what potential issues can arise. Have a quick thought about the boundary conditions, but not get into too many details at this first stage.
- Create the geometry. Depending on the FE package you use, you may find its pre-processor easy to use or maybe you will prefer to use other tools such as CAD software.
- Generate the mesh. As it was stated earlier in this post, try to start with a coarse mesh in order to obtain a fast preliminary solution. Then think about different aspects of the mesh, including:
- Sensitivity analysis.
- Mesh quality.
- Structured vs unstructured mesh.
- Create the properties for your model. Depending on your particular problem, different material models will be available. Every model needs different parameters and offers different advantages. For instance, for simulating composite materials, LS-DYNA offers a wide range of material cards, but not all of them (almost none) are suitable for analysing delamination in an effective way. If you are not sure about which option will provide the most accurate results, you can always do different studies and compare them.
- Define the loads and boundary conditions. It is now when you have to be careful about the boundary conditions and constraints that you apply in order to obtain a real physical behaviour.
- Post-process the results. In order to do a quick check, compare them, whenever possible, with hand calculations.
- Look for obvious errors and why they may be occurring. Then, refine your model.
- Validate the model. You may be able to find some results in the literature. Otherwise, if you want to verify your simulations, you will probably have to conduct experimental tests. Then your model will be able to be extrapolated to other problems, bearing in mind its potential weaknesses for some kind of studies (remember that you have idealised the problem!).
I hope you found this “informal”introduction useful! I will be posting more things about FEA in general and some specific tips based on my experience. Please feel free to comment and suggest any topic you would like me to cover in the weeks to come.