Module 4 : Nonlinear elasticity
  Lecture 27 : Theory of incremental stresses (Contd...)
 


Figure 27.2

Then we can think of equilibrium of a triangular element adjacent to the boundary as shown the figure,

(27.2)

Considering that other external force acting on the body are the body forces, we can write the equilibrium relation

(27.3)

Notice that here “” denotes the length of the contour and “” denotes the area of the surface area. Substituting the expression in equation 13.9 in 13.10 and the using following expressions for  and

(27.4)

We obtain the following expression for the first integral in equation 27.3:

(27.5)