Michell trusses in two dimensions as a Gamma-limit of optimal design problems in linear elasticity
(2017) Calculus of Variations and Partial Differential Equations — Vol. 56, n° 166 (2017)
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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 Γ-convergence, is a certain Michell truss problem. This proves a conjecture by Kohn and Allaire.
- Affiliations
Universität Leipzig
Citations
Olbermann, H. (2017). Michell trusses in two dimensions as a Gamma-limit of optimal design problems in linear elasticity. Calculus of Variations and Partial Differential Equations, 56(166). https://hdl.handle.net/2078.5/53961 (Original work published 2017)