Solving techniques
The finite element method

Geometric non-linear behavior is a complex phenomenon that is difficult to take into account in numerical solutions. Indeed, the stability of the solution strongly depends on the slenderness of the structure and the algorithms used.

Today, total and updated Lagrangian descriptions are the main tools used to solve non-linear problems in solid mechanics. It should be noted, however, that commercial software is now powerful enough to handle the majority of complex industrial cases combining different types of non-linearity.

As mentioned above, non-linearity makes it impossible to describe a direct relationship between the final state of stress and strain. This is why, in order to follow the loading trajectory, the total load {F} is decomposed into a number of increments {ΔF}, chosen small enough to ensure convergence. It should be noted, however,...