27.1 : 应变能

Consider a rod fixed at one end and subjected to an axial force at the free end, which induces stress and leads to elongation in the rod. 

As the axial force is increased, the elongation increases. The plot of axial force versus elongation results in a characteristic load-deformation plot.

The work done by the axial force, as the rod elongates by a small amount, is the product of the axial force and the corresponding elongation.

This work equals the area under the deformation plot, the width of which equals the small deformation.

The total work done can be calculated by integrating the equation within the elongation limits and is equal to the area under the load-deformation curve within the same elongation limits.

The total work done on the rod represents the energy input to the system, known as the strain energy.

Within the elastic limit, the axial force is proportional to the amount of elongation. So, the strain energy is proportional to the square of the elongation.