ON PRINCIPLE OF MINIMUM POTENTIAL ENERGY IN ELASTICITY FROM DEFORMATION OF BARS SUBJECTED TO TENSION

The principle of minimum potential energy in elasticity is comparatively difficult to understand. In this paper, by variational analyses on elastic potential energy, external force potential energy and total potential energy of elastic bars subjected to tension, it is obtained that the variation of total potential energy is the second order infinitesimal of the displacement variation or strain variation. Furthermore, when the displacement variation or strain variation equals to zero, the total potential energy reaches the minimum. The principle of minimum potential energy is thereby examined by the analysis of deformation for elastic bars under axial forces, which is helpful to profoundly understand the principle of minimum potential energy in general.