Material Optimization for Nonlinearly Elastic Planar Beams
Peter Hornung, Martin Rumpf, Stefan Simon
TL;DR
This paper studies how to optimally distribute soft and hard materials in nonlinear elastic planar beams under gravity, proving the optimal distribution is ordered without microstructure and confirming this with numerical simulations.
Contribution
It establishes the optimal material distribution is ordered and free of microstructure for nonlinear elastic beams under gravity, supported by theoretical proof and numerical validation.
Findings
Optimal distribution involves no microstructure.
The distribution is ordered.
Numerical simulations confirm theoretical results.
Abstract
We consider the problem of an optimal distribution of soft and hard material for nonlinearly elastic planar beams. We prove that under gravitational force the optimal distribution involves no microstructure and is ordered, and we provide numerical simulations confirming and extending this observation.
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