The topological derivative of stress-based cost functionals in anisotropic elasticity

The asymptotic perturbation of J is shown to be of order O(a3) for a wide class of stress-based cost functionals having smooth densities. The topological derivative of J, i.e. the coefficient of the O(a3) perturbation, is established, and computational procedures then discussed. The resulting small-inhomogeneity expansion of J is mathematically justified (i.e. its remainder is proved to be of order o(a3)). Several 2D and 3D numerical examples are presented, in particular demonstrating the proposed formulation of DJ on cases involving anisotropic elasticity and non-quadratic cost functionals.