Discussions on the expressions of external force work and its related problems

Work of external forces and potential energy are key concepts in elastic mechanics of continuum. But it is found by the author that the expressions of these concepts listed in some classic textbooks are not real, which is verified using theorem of strain energy and then explained with an example of 1 dimension spring. Then the definitions and the relationships of total potential energy, potential energy / work of external forces and the reserved forces are analyzed, which make it easily for the primer students to understand these concepts clearly. At last, an advice is given that it is proper and necessary to tell clearly the fact that the expressions above are not real.