Feature sensitivity: A generalization of topological sensitivity

Shape and topology optimization have flourished over the last two decades, resulting in a number of powerful mathematical concepts. One such concept is that of topological sensitivity that quantifies the impact of adding infinitesimal holes (within a given continuum) on specific quantities of interest such as compliance, average stress, etc. In this paper we explore a novel generalization of topological sensitivity called feature sensitivity that captures the first-order change in quantities of interest when an arbitrary internal and boundary feature is created within an existing continuum. Specific algorithms are derived for computing the feature sensitivity of linear elasticity problems, and illustrated through numerical experiments.