On the existence of optimal shapes in architecture
Analysis of PDEs
2020-10-06 v1 Mathematical Physics
Functional Analysis
math.MP
Optimization and Control
Abstract
We consider shape optimization problems for elasticity systems in architecture. A typical question in this context is to identify a structure of maximal stability close to an initially proposed one. We show the existence of such an optimally shaped structure within classes of bounded Lipschitz domains and within wider classes of bounded uniform domains with boundaries that may be fractal. In the first case the optimal shape realizes the infimum of a given energy functional over the class, in the second case it realizes the minimum. As a concrete application we discuss the existence of maximally stable roof structures under snow loads.
Keywords
Cite
@article{arxiv.2010.01832,
title = {On the existence of optimal shapes in architecture},
author = {Michael Hinz and Frédéric Magoulès and Rozanova-Pierrat Anna and Marina Rynkovskaya and Alexander Teplyaev},
journal= {arXiv preprint arXiv:2010.01832},
year = {2020}
}