Most of the structural dimensioning procedures start with linear static calculations, at least during the preliminary validation. These are based on steady equilibrium between external loads (forces, pressure, accelerations) and the state of deformation of the test system, assuming linear elastic constitutive behavior of the material and linear relationship between strain and displacement components.
However, to fully understand the behavior of a physical mechanical system, and then to be able to manage the mode of failure and optimize the design, it is necessary to take into account phenomena such as:
contact between different bodies, as in bolted connections
plastic deformations
non-linear buckling and post-buckling behavior
A detailed analysis of all these aspects require dropping the linearity assumption and the adoption of nonlinear finite element analysis techniques.
