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arXiv · 1703.05989

Michell trusses in two dimensions as a Gamma-limit of optimal design problems in linear elasticity

Heiner Olbermann
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Abstract

We reconsider the minimization of the compliance of a two dimensional elastic body with traction boundary conditions for a given weight. It is well known how to rewrite this optimal design problem as a nonlinear variational problem. We take the limit of vanishing weight by sending a suitable Lagrange multiplier to infinity in the variational formulation. We show that the limit, in the sense of $\Gamma$-convergence, is a certain Michell truss problem. This proves a conjecture by Kohn and Allaire.

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Heiner Olbermann. 2017-03-17. Michell trusses in two dimensions as a Gamma-limit of optimal design problems in linear elasticity. https://arxiv.org/abs/1703.05989

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