  In this paper a treatment of hypersingular integral equations, which have
relevant applications in many problems of wave dynamics, elasticity and fluid
mechanics with mixed boundary conditions, is presented. The main goal of the
present work is the development of an efficient direct numerical collocation
method. The second part of the work is devoted to the application of the method
to the porous elastic materials. This part deals with classical problem for
cracks dislocated in a certain very specific porous elastic material, described
by a Cowin-Nunziato model. By applying Fourier integral transform the problem
is reduced to some integral equations. For the plane-strain problem we operate
with a direct numerical treatment of a hypersingular integral equation. We also
study stress-concentration factor, and investigate its behaviour versus
porosity of the material. At the end we investigate the possibility to extend
the results in the thermoelastic case.
