Principle of Virtual Work and Minimum Potential Energy (P.E.)

Introduction:

The Total Potential Energy is nothing but the energy due to Strain Energy (internal work done) and Work potential of a force (external work done).

Theorem of P.E.:

Of all the displacements satisfying given Boundary conditions and Equilibrium conditions, the actual displacement is the one that minimizes the total potential energy at stable Equilibrium.

In other words, for stable Equilibrium, for any virtual displacement or variational displacement, change in P.E. is positive always and hence, Potential Energy, got earlier, is the minimum Potential Energy.

This concept of minimum total potential energy is nothing but can be called as the special case of the virtual work principle.

The Detailed explanation of the topic is given in the pdf embedded below with solved examples. Application of Minimum Potential Energy in case of a beam and truss is also explained.
Click here to read about Classical Rayleigh Ritz Method