Computer Aided Engineering (CAE) Finite Element Analysis (FEA) Types continued
Non-linear Statics 
The use of non-linear properties can become very important. Non-linear needs to be used when linear approximations of any of the following characteristics become too inaccurate for the problem in hand. Non-linear may be used to solve problems where there may be a combination of non-linear characteristics. These are;
- material non-linearity,
- geometric non-linearity and
- moving (non-static) boundary conditions.
Materials used may be highly non-linear (stress/strain curve) and exhibit properties such as hyperelastic (elastomers such as rubber), viscoelastic (creep such as glass), elasto-plastic (most metals have elasto-plastic properties but it is not significant most of the time). Material models become very important, and the end solution is only ever as good as the information established at the beginning of the analysis - rubbish in = rubbish out!
Geometric non-linearity is where the stress and strain of the model no longer relate to each other. I.e The stiffness of the model changes under load. The model becomes distorted exhibithing enhanced or reduced stiffness giving stresses that no longer have anything to do with the strain exhibited by the model. Geometric non-linearity is usually interpreted as large deflection, even though this is true, geometric non-linearity may occur under very small deflections/strains.
Moving (or non-static) boundary conditions. Now that we've dicsussed matarial and geometric non-linearity, it should become clear that if the model stiffness and materials are changing under load, then so are boundary conditions. For example, if a load is placed ot the end of a cantilver beam, then that load will no longer be applied with the same vector quantity as the beam deforms under the load.
Non-Linear Dynamic
Pretty much the holy grail of analysis. A combination of all the non-linear and dynamic analysis techniques discussed.