Calculus of Variations and Geometric Measure Theory
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H. Olbermann

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

created by olbermann on 23 Jul 2019

[BibTeX]

preprint

Inserted: 23 jul 2019

Year: 2017

ArXiv: 1703.05989 PDF

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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