## A brief introduction to Finite Element Analysis

Have you ever come across the term “FEA” or “FEM” when talking about structural analysis? If you have and you still don’t understand  what it means and how it works, this post is for you. Don’t be afraid, no scary equations are presented here!

Finite Element Analysis (FEA), or Finite Element Method (FEM), can be defined as a methodology for solving field problems using numerical approaches. This kind of problem needs the determination of a spatial distribution and this can be seen, for instance, as the distribution of temperature in the piston of an engine. From a mathematical point of view, a numerical solution of a field problem is defined by differential equations or by integral expressions.

This method divides our structure or component in a certain number of small pieces, called elements, resulting in a meshed structure where the elements are connected at “nodes”. In contrast with the real world, in each element a field quantity can only present a simple spatial variation (e.g. described by a polynomial). Therefore, what we are obtaining is an approximation of the expected result or, in other words, a prediction of the behaviour which the component will show when subjected to different conditions. When all the elements which are part of the mesh are assembled we deal with what is known as “finite element structure”. The mesh is represented by a system of equations which has to be solved for unknowns at the previously mentioned nodes. These unknowns can be seen as the value for a field quantity. Hence, when these “partial” solutions are combined, the complete field variation is determined. Therefore, the quality of the final solution is highly dependent on the number of elements which are used. However, using an extremely big number of elements means that the computer will need much more time to calculate a solution. Bearing in mind that the engineer has to be aware of the problem that needs to be solved, it is his own experience and expertise what will define a good balance between the quality of the approximation and the computational cost.

“Even a child can learn how to create FE models and how to run simulations and obtain results”

Apart from that, with regards to the numerous advantages of FEA, it is worth to mention the following ones:

• It is applicable to any field problem (i.e. stress, displacement…).
• There are no restrictions regarding geometry, loads or boundary conditions.
• Parts made of different typologies (i.e. different mathematical descriptions) can be combined.
• It resembles the actual region to be investigated.

To sum up, it is important to say that nowadays there are a lot of software packages which are capable of calculating solutions for FE problems. Nevertheless, it is also remarkable that even a child can learn how to create FE models and how to run simulations and obtain results. This highlights the fact that deep knowledge and experience are necessary in order to use this powerful tool in an effective way, as the programme can provide embarrassing results if the user only knows how to introduce parameters and does not understand what the software is doing and why certain things need to be defined in specific cases.

Source: ‘Concepts and Applications of Finite Element Analysis’ by R. D. Cook, D. S. Malkus, M. E. Plesha and R. J. Witt (2002)