Assumption 1: Since the bending is small the normal vector to any point on the bent plate is along the z-axis.

Assumption 2: Since the plate is thin it bends very easily, so that a very small amount force needs to be applied on the surface of the plate, much smaller than the internal stresses produced by the stretching and compression of its parts. Hence we safely neglect the surface forces leading to , i.e. . However these quantities must be small within the plate if they are zero on the surface. Hence it can be concluded that these stress components are negligibly small with respect to the other components of the stress tensor. Thus we have,

(16.1)

Putting , the components of displacement are obtained as,

(16.2)

and the components of the strain tensor are:

(16.3)

The free energy per unit volume is,

(16.4)

Total free energy of the deformed plate of thickness is,

(16.5)