The minimum total potential energy principle is a fundamental concept used in physics and engineering.
The equality between external and internal virtual work (due to virtual displacements) is: where In the special case of elastic bodies, the right-hand-side of (3) can be taken to be the change,
, of elastic strain energy U due to infinitesimal variations of real displacements.
where the minus sign implies a loss of potential energy as the force is displaced in its direction.
The variational form of (2) is often used as the basis for developing the finite element method in structural mechanics.