the velocity solution in the principle of virtual power and the displacement solution in the principle of virtual work

In Dr. Ted Belytschko's book, Nonlinear Finite Elements for continua and Structures, he uses two formulations to describe the Lagrangian mesh, i.e., Total Lagrangian formulation(TL) and Updated Lagrangian formulation(UL). For TL formulation, he derives the weak form using the principle of virtual work, which will result in a finite element formulation whose unknowns are displacement. For UL formulation, he gets the weak form using the principle of virtual power, which leads to a finite element formulation whose unkowns are velocity.

My question is:

In nonlinear static problem, we just care about the displacement. If I use the UL formulation to derive the Lagrangian element. How should I transform the velocity solution to the displacement solution? Because in static prolem, there is no time step.

I am kind of new to the UL formulation. Looking forward to experts giving me some comments. 
Thanks.