Steve Roensch, President of Roensch & Associates and metallurgy expert witness, discusses Finite Element Analysis:
FEA is applied to many types of problems, such as temperatures in consumer electronics, airflow around aircraft, and magnetic fields in electric motors. By far the most common application is structural FEA — determining how a solid body responds to various forces.
The structural problem amounts to writing down some “governing equations” that describe the material and how it behaves, and then solving those equations for the physical part being analyzed subject to how it is held and loaded. This can be done on paper for some simple part shapes. The resulting “closed form solution” is another equation that provides the answer in terms of the basic variables, such as the part’s dimensions.
But reality intervenes, and most parts are too complicated to solve in closed form. FEA comes to the rescue by providing a “numerical solution” for each individual problem. This is a large gathering of numbers approximating the desired answers, such as displacements and stresses, across the part. But each solution is unique to a specific case; there is no simple answer in equation form.