Justify that the edge dislocation solution (15.1.2) provides the required multivalued behavior for the displacement field. Explicitly

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Justify that the edge dislocation solution (15.1.2) provides the required multivalued behavior for the displacement field. Explicitly develop the resulting stress fields given by (15.1.3) and (15.1.4).

Equation 15.1.2

U V= b 2 tan b 2 1 xy x 2(1  v) x + y -1 2+ 1 - 2v 4(1-V) -log(x + y) 1 J 2(1  v) x + y

Equation 15.1.3

BY (3x + y) (x + y)  0x = -bB: Oy=bB(x - y) (x + y)  Txy = bB x (x - y) (x + y) 0 = v(ox + ay) Txz = Tyz = 0

Equation 15.1.4

0r = 08: or Tra bB r bB r -cos f -sin

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