Page 352 - Introduction to Continuum Mechanics

336 The Elastic Solid

(b) Suppose that a sphere of 5 cm radius is under the influence of this stress field, what will be
the change in volume of the sphere? Use the elastic constants of Prob.5.9.
5.11. Show that for an incompressible material (v = 1/2) that
(a)

(b) Hooke's law becomes

5.12. Given a function/(a, b} = ab and a motion

and

? 7
5.13. Do the previous problem for/(a, b} = a + b
5.14. Given the following displacement field

(a) Find the corresponding stress components.
(b) In the absence of body forces, is the state of stress a possible equilibrium stress field?
5.15. Repeat Problem 5.14, except that the displacement components are

ui = kX 2X 3, u 2 = kX 1X 3, u 3 = kX 1X 2t k = 10~ 4
5.16. Repeat Problem 5.14, except that the displacement components are:
4
«i = -kX 3X 2, u 2 = kXiX-$, u 3 = ksinX 2, k = 10~

5.17. Calculate the ratio of c^/c^for Poisson's ratio equal to -, 0.49, 0.499