Elastic Solutions in Terms of Greens Functions

What will determine the complexity of (2.2.1) is the nature of the co dependence of the elastic solutions. The simpler this dependence is, the easier it will be to determine u r, co, t) and 0- The question is, what deter- 

The basic idea behind the approach outlined here was proposed in a general form by Graham and Sabin (1973), though earlier papers, for example Graham (1968) and Ting (1969), contained similar concepts, in less general form. 

The Green s function formalism for non-inertial elastic problems will now be used to express uf (r, 03, t), CO, t) at any point in the body, in terms of specified surface quantities. The development of this formalism is standard and will not be discussed here. We refer to the treatment by Lardner (1974) for example. Really, all that is required in the present context is that the displacements and stresses can be expressed as space integrals of the boundary functions. 

The Green s functions will be attributed a dependence upon co to indicate that the moduli have been replaced by the complex moduli. We will omit subscripts, in this and the next two sections, which amounts to developing a one-dimensional rather than a three-dimensional theory. This results in a considerable tidying of the equations and the loss of generality is irrelevant in the present context, because only the one-dimensional theory is required, in any case, in later chapters. This is because attention is focussed on crack and half-space problems of such a nature that only the normal displacement and pressure are relevant to the solution of the problem. 

It is not difficult to generalize the discussion, in a formal sense, to three dimensions. The Green s functions become rank two tensors. However, if the 

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