Riks method (arc-length method) in only prescribed displacement boundary condition.

[gongym]

The formulation of the arc length method is as follows:

where,

Where q vector is the external force.
My question is how do we define this q vector with only prescribed displacement boundary condition?

 

[FEA way]

Riks procedure solves for loads and displacements simultaneously (both are treated as unknowns).

You can find more information about the implementation of this method in Abaqus documentation chapters "Unstable collapse and postbuckling analysis" and "Modified Riks algorithm".

 

[gongym]

First of all thank you for your reply

However, I already saw ABAQUS manual.

And there are no any info about the only prescribed displacement boundary condition case.

So if you know other references about the formulation of arc length solver in prescribed displacement case then please help me