I'm reading a book on the finite element method. Specifically I'm looking at the background material where they are discussing potential energy, equilibrium, and the Rayleigh-Ritz method.
The book claims that potential energy is equal to strain energy + work potential energy. I see that strain energy is like spring energy from a spring being stretched or compressed, however I don't see what work potential represents. I feel that if a spring system is perturbed via forces, the work input into the system should be equal to the amount stored in the springs. (By integrating f(x) over x). The book seems to suggest otherwise since they are simply multiplying the force applied in the equilibrium position, times the displacement.
What's going on here, and especially what is the intuitive meaning behind work potential?