Virtual Work Principle

The principle of virtual work is a variational statement of equilibrium. It states that, for an admissible virtual displacement field, the internal virtual work equals the external virtual work.

In finite element analysis, this principle provides the weak form of the governing equations. The weak form is especially useful because it reduces differentiability requirements and naturally supports element-wise approximation.

For a linear elastic static problem, the weak form leads to the element stiffness contribution:

K_e = integral_over_element( B^T D B dV )

and the element force contribution:

f_e = contributions from body forces, surface tractions, and nodal loads

The global system is obtained by assembling element contributions over the full mesh.