Generalized Boussinesq Formula

The problem of a circular specified load of fixed radius moving at uniform velocity over two- and three-layer viscoelastic media, in the context of pavement design, is considered by Battiato et al. (1977) and Battiato et al. (1982), using the Correspondence Principle. 

In the non-inertial case, penny-shaped cracks have been considered by Graham (1970). No new result of physical or methodological significance emerges that has not been observed for plane cracks. Sabin (1975) treats inertial penny-shaped cracks. 

We will write down the displacement-traction relationship on the boundary that will form the basis of the considerations of this chapter. This is essentially the solution of the stress boundary value problem, discussed in Sect. 3.2 in the plane case. We shall neglect surface shear, however, so that the required relationship is a generalization to Viscoelasticity of the classical Boussinesq relationship. Its form follows directly from the elastic result by invoking the Classical Correspondence Principle. A more explicit derivation may be found in Hunter (1961) and also Golden (1978), who includes a shear traction term. Letting 

As in the plane case, there will be an apparently total emphasis on boundary quantities, to the exclusion of discussion of the behaviour of the various quantities in the interior of the body. There is no fundamental reason for this other 

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