Michell truss type theories as a $\Gamma$-limit of optimal design in linear elasticity

Abstract

We show how to derive (variants of) Michell truss theory in two and three dimensions rigorously as the vanishing weight limit of optimal design problems in linear elasticity in the sense of $\Gamma$-convergence. We improve our previous results in that our treatment here includes the three dimensional case and that we allow for more general boundary conditions and applied forces.