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