Page 348 - Introduction to Continuum Mechanics

332 The Elastic Solid

The equations of equilibrium are:

Noting that Jj and /2 ( and therefore <p\ and $2), are functions of r only, we obtain, from the
second and the third equations of equilibrium,

That is, p is a function of r only. Thus,

From the first equation of equilibrium, we have

The total normal force N on a cross sectional plane is given by

To evaluate the integral, we first need to eliminate p from the equation for T^. This can be
done in the following way:
With

we have

Now, in view of Eq. (ii), we have
t/-n