Sources of Non-linearity

There are two different types of sources of non-linearity. These two main sources are the geometric and the material non-linearity. 

Geometric non-linearity (GNA, GNLA) #

Geometric non-linearity takes into account the large displacement and large rotation of structural elements. The displacements are not simply superposed to the original geometry but the nodes are really moving during the calculation. Due to deflection, normal forces appear in initially bended structures. The equilibrium equations are written for the deformed geometry and the displacement of the application point of loads are also considered. However, in AxisVM the loads do no not rotate with the node or element, on which they applied. This is known as a non-follower or conservative load.

Material non-linearity (MNA, MNLA) #

Any other types of sources of non-linearity are called to material non-linearity.

One of these is actually the non-linearity of structural elements due to their non-linear material.

Discrete elements with non-linear behaviour also belong to this group. These are e.g. trusses, supports, links and hinges with tension only or compression only behaviour or with limit force. Moreover, springs, supports, links and hinges with non-linear or plastic characteristics. And also the gap elements. To take their non-linear behaviour into account, the material non-linearity option must be enabled.

Geometrically and materially non-linear analysis (GMNA, GMNLA) #

Classification of non-linearities #

The following table classifies the different types of non-linearities according to which phase of the calculation they start to work.

Most non-linearities start working after a limit of strain or internal force, as it is shown in the first two rows of the table. Yielding of material, cracking of RC, truss with limit force, closing of a gap, hinge with slack or support with backlash are in this group. They are usually modeled with simplified characteristics, of which beginning part is linear. Therefore, in case of these types of non-linearities, weak convergence is expected only at higher load levels.

Tension-only and compression-only behaviour, introduced in the third row of the table, has a break in the stress-strain or force-displacement curve at the origin. This switch-like non-linearity works immediately at the beginning of the load process. Therefore, weak convergence is expected in the first increment. Kicking-off the calculation can be difficult. Many iterations may be necessary to find the right tensioned-compressioned configuration of these kind of trusses and supports. Application of soft-starting increment function can help to kick-off the calculation.

The fourth row of the table displays the geometric non-linearity, which is a continuously working non-linearity. It can be just a soft non-linearity if the load level is far from the loss of stability of the structure or of a part of that. However, working together with other non-linearities, it can cause weak convergence. In such a mixed case, trial calculations with only material and with only geometric non-linearity can be helpful to find the root cause of weak convergence. This may be purely numerical, but it may also be a matter of reaching the limit strength of the structure.