A structure theorem for shape functions defined on submanifolds

摘要

In this paper, we study shape functions depending on closed submanifolds. Weprove a new structure theorem that establishes the general structure of theshape derivative for this type of shape function. As a special case we obtainthe classical Hadamard-Zol\'esio structure theorem, but also the structuretheorem for cracked sets can be recast into our framework. As an application weinvestigate several unconstrained shape functions arising from differentialgeometry and fracture mechanics.