# Virtual Power Term Names

It is possible to give a physical name to each of the terms in the virtual power equation. This will be useful in the development of finite element equations. The nodal forces in the finite element equations will be identified according to the same physical names.

You have used the decomposition of the velocity gradient $L$ into its symmetric and skew symmetric parts and that $\delta {W}_{ij}{\sigma}_{ji}=0$ since $\delta {W}_{ij}$ is skew symmetric and ${\sigma}_{ji}$ is symmetric.

for all $\delta {v}_{i}$ admissible.

We can show that virtual power principle implies strong equations of equilibrium. So it is possible to use the virtual power principle with a suitable test function as a statement of equilibrium.

The virtual power principle has a simple physical interpretation. The rate of work done by the external forces subjected to any virtual velocity field is equal to the rate of work done by the equilibrating stresses on the rate of deformation of the same virtual velocity field. The principle is the weak form of the equilibrium equations and is used as the basic equilibrium statement for the finite element formulation. Its advantage in this regard is that it can be stated in the form of an integral over the volume of the body. It is possible to introduce approximations by choosing test functions for the virtual velocity field whose variation is restricted to a few nodal values.