The topological asymptotic analysis provides the sensitivity of a given
shape functional with respect to an infinitesimal domain perturbation, like
the insertion of holes, inclusions, cracks. In this work we present the
calculation of the topological derivative for a class of shape functionals
associated to the Kirchhoff plate bending problem, when a circular inclusion
is introduced at an arbitrary point of the domain. According to the
literature, the topological derivative has been fully developed for a wide
range of second-order differential operators. Since we are dealing here with
a forth-order operator, we perform a complete mathematical
analysis of the problem.