Show that the general plane strain edge dislocation problem shown in Fig. 15.3 can be solved using methods of Chapter 10 with the two complex potentials:

where b = b_x + ib_y. In particular, verify the cyclic property [u + iv]_C =–b, where C is any circuit in the x,y-plane around the dislocation line. Also determine the general stress and displacement field.

Fig 15.3

Y(z) = iub 4T (1-v) - log z, (z) = iub 4T (1-V) -log z