Question: 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)

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

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]

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