EXAMPLIFICATION OF THE PRINCIPLE OF MINIMUM POTENTIAL ENERGY FOR PLANE PROBLEMS OF STRUCTURAL MECHANICS

The principle of minimum potential energy is an advanced part of structural mechanics, whose complete introduction is rarely seen in this subject. This paper discussed the application of canonical equations in displacement method when considering the bending deformation for beam with constant stiffness. On this basis, the dual relationship between the potential energy method and the displacement method was analyzed. It is concluded that under the balanced force composed of in-plane loads and support reactions, the possible small displacement of the beam is controlled by the equation of virtual force. Meanwhile, if the real displacement can also be solved by using the superposition principle, then the total potential energy at the real displacement will be the minimum. The principle of minimum potential energy is thereby examined by the analysis of bending deformation for beam of constant stiffness, which is helpful to understand the principle of minimum potential energy in general.