Mathematics of Floating 3D Printed Objects
ORAL
Abstract
We explore the stability of floating objects through mathematical
modeling and experimentation. Our models are based on standard ideas of
center of gravity, center of buoyancy, and Archimedes' Principle. We
investigate a variety of floating shapes with two-dimensional cross sections
and identify analytically and/or computationally a potential energy landscape that
helps identify stable and unstable floating orientations. We additionally explore
the influence of changing an object's center of gravity. For objects with square
cross section, for example, this breaks the symmetry observed in the uniform density case.
We design and create 3D printed objects, float them, and compare the observations
to the theoretical predictions.
modeling and experimentation. Our models are based on standard ideas of
center of gravity, center of buoyancy, and Archimedes' Principle. We
investigate a variety of floating shapes with two-dimensional cross sections
and identify analytically and/or computationally a potential energy landscape that
helps identify stable and unstable floating orientations. We additionally explore
the influence of changing an object's center of gravity. For objects with square
cross section, for example, this breaks the symmetry observed in the uniform density case.
We design and create 3D printed objects, float them, and compare the observations
to the theoretical predictions.
–
Publication: D. M. Anderson, B. G. Barreto-Rosa, J. D. Calvano, L. Nsair, and E. Sander
``Mathematics of Floating 3D Printed Objects," https://arxiv.org/abs/2204.08991
to appear in Proceedings of Symposia in Applied Mathematics (PSAPM): Short Course on 3D Printing: Challenges and Applications (2023).
Presenters
-
Brandon G Barreto-Rosa
- George Mason University