Finite Element Analysis is a method that is mostly used within the aerospace industry to create load models. Sometimes, it is also used to form highly detailed stress models. To put it together even more simply, Finite Element Analysis can be summarized within this one formula:
In this formula, F is the symbol for the applied force, the K in the title stands for the stiffness of the entire created structure, and X denotes the displacement, which is unknown. Sometimes, the Symbol K is also known as the “global stiffness index”, which means the stiffness of the entire or global combined structure. It is assembled with many little pieces of discretized stiffness and then used to create one big stiffness index. The size of the matrix can vary depending on the model. The numerical simulations for the complex stiffness of any complex structure are only possible via Finite Element Analysis and modeling.
In this analysis equation, the known quantities are the applied force (F) and the stiffness of the created structure (K), which automatically includes the constraints for the static equilibrium. That only leaves us with one unknown quantity, that being the displacement (X) and its related quantities. This is where the ‘Finite Element Solver’ is brought in. This Solver’s job is to:
- Compile all the numerical data in the model.
- Assemble the complete global stiffness index.
- Ensure that the model being worked upon is numerically defined correctly and is balanced with the correct loads and constraints.
- Invert the large stiffness matrix and spawn all the necessary equilibrium equations.
- Solve all the created equations and locate the unknown displacements.
- Calculate all the derivative quantities, such as strains, stresses, etc. after solving the unknown displacements.
Even after the analysis, it is of prime importance that the results are checked thoroughly by an analyst to ensure that they make sense. One should always look at the deformed plot and make sure that the deformations are correct and make sense. Make sure the model behaves as expected. Go ahead and take a look at the max displacement value and ensure that it makes sense as well. You should do some hand calculations using the beam theory to ensure that the reactions make some sense and so on.
While it is fairly easy to be impressed by the pretty colors of FEM results, it can be fairly dangerous in the hands of a person who entirely depends upon the workings of FEM, for the FEM model is only as accurate as the input that is fed in it. Hence, the checking and preparation of results are of vital importance. But even then, with its drawbacks, it is quite an invaluable tool, nay, a resource in today’s analysis sector. Even in interviews for related jobs, finite element analysis interview questions can be asked, so be well prepared for that.
This concludes the basic knowledge-induced article about what exactly is Finite Element Analysis. We hope that the article was somewhat informative and helped answer a few questions you may have about this method. Also, you can find CFD online courses that you can take up.