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

TL;DR

This paper rigorously derives Michell truss theories in 2D and 3D as the limit of optimal design problems in linear elasticity, extending previous results to more general conditions.

Contribution

It provides a rigorous derivation of Michell truss theories as a $ ext{Gamma}$-limit in both two and three dimensions, including more general boundary conditions and forces.

Findings

Michell truss theories obtained as $ ext{Gamma}$-limits of optimal design problems

Extension to three-dimensional cases

Inclusion of general boundary conditions and applied forces

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.