Page 209 - Introduction to Continuum Mechanics

194 Stress

thus,

Example 4.9.2

It is known that the equilibrium stress field in an elastic spherical shell under the action of
external and internal pressure in the absence of body forces is of the form

(a) Verify that the stress field satisfies the equations of equilibrium in the absence of body
forces.
(b) Find the stress vector on spherical surface r=a.
(c) Determine A and B if the inner surface of the shell is subjected to a uniform pressure PJ
and the outer surface is free of surface traction.

Solution.
(a)

Thus, Eq. (4.8.2a) is satisfied when B r = a r= 0, Eqs. (4.8.2b) and (4.8.2c) can be similarly
verified, [see Prob.4.38].
(b) The unit normal vector to the spherical surface is n = e p thus the stress vector is given by

i.e.,