Consider the antiplane strain problem of a distributed loading F (per unit length) along the entire z-axis of an infinite medium. This will produce an axisymmetric deformation field. Using cylindrical coordinates, show that in the absence of body forces, governing equation (7.4.5) will reduce to

Solve this equation to determine the form of the displacement and then show that the stresses are given by   

d'w 1 dw + dr r dr = 0