Séminaire de Karol Bołbotowski (Faculty of Civil Engineering, Warsaw University of Technology, Poland)
From optimal plane membranes to optimal 3D vaults
Abstract : Designing a stone or masonry vault that through pure compression efficiently transfers the loading to the bearing columns is one of the oldest challenges in architecture and structural engineering. In the late ‘70s an attempt was made to optimize such surface structures within a framework that is reminiscent of the renown Michell problem. So far, however, there was no clear mathematical formulation available, and the progress was mainly numerical. In this talk we put forth a new link between the optimal vault problem and the novel 2D problem of designing an optimal membrane. The latter problem has been recently discovered to remarkably connect with the Monge-Kantorovich optimal transport problem. We shall prove that the surface on which the perfect vault should concentrate equals the deflected optimal membrane, whilst the vault’s material distribution may be found through unprojecting the one of that membrane.