I am trying to apply displacement difference as an external load at node pairs within static elastic FE model. I can not simply impose some displacement and fix their degrees of freedom, as this will not allow one pair of nodes displace regarding the other pairs. On the other hand, prescribing displacement and not blocking dofs leads to the solver erasing the imposed displacement.
Is there a way to have this delta between two nodes without fixing their exact position in space (maybe including periodicity)?
Yes there is.
As an approximate approach, this can be done by connecting the two nodes with a very hard spring of zero length and then applying forces to nodes enough to cause the desired difference. The force should be applied to both nodes and in opposite directions. This is applicable if we know the direction of displacement.
In general this is a constraint problem and requires nonlinear iteration. This can be considered a particular contact of tied contact with initial gap.
There is two methods: penalty augmentation and Lagrange multiplier adjunction
read this article for explanation
http://kis.tu.kielce.pl/mo/COLORADO_FEM/colorado/IFEM.Ch09.pdf
A non-linear analysis can be utilized for the approximate method. A rigid spring with marginal depth can be utilized to joint the two nodes. The magnitude of the applied forces must enough to induce the required variance.
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