Nonlinearities in structural mechanics

Two years have already gone in the preparation of this thesis and now it seems in order to pass to the next part: the study of stochasticity.
Altogether with the preparation of our next article I am already summarizing and setting things up for the account for uncertainties in the structural design.
For such purpose, and after so much research into elasticity, dynamics and numerical methods, I have done the following scheme where most of the nonlinearities (which not surprisingly are often associated to randomness) can be fit into.
The scheme is based on the ubiquitous "Governing Equations" that serve as basis for every mechanician.

  • System's internal balance equations (Statics or dynamics)
    • Nonlinear damping
  • Constitutive equations (Material)
    • Plasticity
    • Viscosity
    • Creeping
    • Hiperelasticity
  • Kinematic equations (Geometry)
    • Large deformations with small strains
    • Large strains
    • Buckling
    • Instability
  • Boundary conditions
    • Forces
      • Pressure
      • Loads
      • Wind
      • Waves
      • Friction
    • Displacements
      • Contact
      • Link rupture

In the following months I will try to expand this list at the same time as I will try to understand how these nonlinearities are tackled in a deterministic manner.

The main point of my thesis is that stochastic methods are way more suitable for this purpose than deterministic ones...we will see...:)

Soon I will be getting back to my loved Ljubljana for a while, far from noisy Barcelona...