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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 Γ-convergence. We improve our results from [H. Olbermann, Michell trusses in two dimensions as a Γ-limit of optimal design problems in linear elasticity, Calc. Var. Partial Differential Equations 56 2017, 6, Article ID 166] in that our treatment here includes the three-dimensional case and that we allow for more general boundary conditions and applied forces.

Michell truss type theories as a Γ-limit of optimal design in linear elasticity