What is FEM?

The finite element method (FEM) is a numerical technique for calculating stresses, deformations, temperatures, and other physical quantities in structures. It's used whenever the geometry or loading is too complex for a closed-form analytical solution.

The core idea

FEM divides a complex structure into many small, simple pieces called finite elements. For each element, the equations of equilibrium are easy to solve. The elements are connected at nodes — shared points where displacements and forces are exchanged between elements. Assembling all the elements gives a large system of equations that the solver resolves simultaneously.

The result is an approximation of the true solution. The finer the mesh, the better the approximation — but also the longer the computation.

What FEM can calculate

• Stresses and strains — is the material strong enough?
• Displacements — how much does the structure deflect?
• Natural frequencies — at what frequencies does it vibrate?
• Temperatures — how does heat flow through the structure?
• Contact forces — how are forces transferred between parts?

What FEM cannot do

FEM gives you the answer to the question you asked, with the geometry you modelled, and the loads you applied. It cannot:

• Tell you if the question was the right one
• Compensate for a wrong boundary condition
• Detect a load case you forgot to consider

The engineering judgement that goes into the setup is just as important as the computation itself.

Linear vs nonlinear analysis

Linear static analysis assumes small deformations and linear material behaviour. The solution scales proportionally with the load — double the force, double the stress. This covers the large majority of structural design checks.

Nonlinear analysis is needed when:

• Deformations are large relative to the part dimensions
• The material yields (plasticity)
• Contact between parts changes during loading

Linear analysis is always the right starting point — use nonlinear only when you have a specific reason to.