Many algorithms that have been proposed for the numerical evaluation of Cauchy principal value integrals are numerically unstable. In this work we present some formulae to evaluate the known Gaussian quadrature rules for finite part integrals
, and extend Clenshow's algorithm to evaluate these integrals in a stable way.
A theory of bending of elastic plates is considered, in which the effect of transverse shear deformation and transverse normal strain are taken into account through a specific form of the displacement field. It is shown that the system of equilibrium equations is elliptic and that Betti and Somigliana formulae can be established, which permit the solution of the interior and exterior Dirichlet and Neumann problems by means of boundary integral equation methods.
The numerical evaluation of a $2$-D Cauchy principal value integral arising in boundary integral equation methods
