2. A large plate subjected to pure shear =S at remote boundaries contains a rigid

circular inclusion in the region r

is prevented from moving, so that u, = ₂ = 0 at r=a. For this problem, the Airy's

Bsin20

stress function is given by (7,0)=-=

S>* sin 20

2

You could now find

the stress, strain, and displacement components by the usual way, that is, by

differentiating it, (re), with respect to rand e, find strains using Hooke's Law and

then integrate strains to get the displacements. An alternate (and direct) way to get

stresses and displacements is using the Mitchell solutions (Tables 8.1 and 9.1).

a. Find the stress components . . Or using the Mitchell solution (Table 8.1)

and check against those given in equations (8.39-8.41).

b. Write down the displacement components, and using the Mitchell solution

(Table 9.1)

c.

Using the displacement boundary conditions at the elastic plate and rigid

inclusion interface, u, = ₂ = 0 at r = a, determine the constants A and B in the

stress function.

d. Write down the final stress function, stress and displacement components.

+ Asin 20+