Complex Integral Equations of the Direct Approach

The common procedure for deriving the equations of the direct approach is as follows: reciprocal (Betti’s) formula — Somigliana’s identities — integral equations. Certainly, we may try to shorten this way by starting directly from the real Somigliana’s formulae for displacements (8.6) and substituting the complex expressions for kernels and densities into it. In practice this is longer than following the whole chain. Thus we choose to take all the steps. In addition this will provide us with the complex variable form of Betti’s formula, which is important in itself.