UC San Diego

The minimal stress reconstruction problem asks for a sparse structure supporting an input force distribution as well as obstacle constraints. In geometric measure theoretic terms, this corresponds to finding a \textit{varifold} satisfying certain physical constraints on its local and global structure. This thesis describes a method which realises such varifolds by representing them as stress matrices which are the optima of an almost-convex optimization problem over a compact domain. This method is able to successfully generate sparse structures with rich internal structure that support a wide variety of force distributions and obstacles.