1. Definition of geometric non-linearity

The linear analysis of structures implicitly admits three assumptions:

• the material's behaviour is elastic at any level of deformation;

• deformations are infinitesimal;

• the strength of the material is infinite.

These assumptions, which justify linear calculation, are acceptable as long as the effect of loading remains small in terms of stress, strain and displacement. In reality, structural mechanics includes four types of non-linearity, associated respectively with the material, the geometry, the applied forces and the boundary conditions.

Geometric non-linearity is expressed by a significant deviation of the deformed configuration of the structure from its initial configuration (i.e. unloaded configuration), as...