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Heiner Olbermann
Monday 20 January 2020
Heiner Olbermann (Université Catholique de Louvain)
On a quadratic-to-linear Gamma-limit with applications in elasticity
Abstract :
We reconsider the minimization of the compliance of a two- or three-dimensional elastic body for a given weight. It is well known how to rewrite this optimal design problem as a nonlinear variational problem. In order to guarantee the existence of minimizers, the problem has to be relaxed via a suitable quasiconvexification procedure. This has been done by Kohn, Strang and Allaire in the 1980’s. Formally, sending the penalization parameter for the weight to infinity, one obtains a certain L^1-type variational problem, which in engineering goes by the name of Michell truss theory.
In this talk we show how to make this convergence rigorous in the sense of Gamma-convergence. We mention further applications of this analysis in elasticity theory concerning thin elastic shells.