2022
DOI: 10.3390/computation10070113
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Abstract: The packing of different circles in a circular container under balancing and distance conditions is considered. Two problems are studied: the first minimizes the container’s radius, while the second maximizes the minimal distance between circles, as well as between circles and the boundary of the container. Mathematical models and solution strategies are provided and illustrated with computational results.

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Cited by 5 publications
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“…i.e., the packing fraction of a saturated random packing for spheres was found to be [ 10 ] and for disks . To obtain a higher packing fraction, an optimized packing approach is often used in modeling the particulate system [ 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 ]; most of these works are based on mathematical modeling of the relations between geometric objects and thus reduce the optimal packing problem to a nonlinear programming problem. However, the objective of this approach is to obtain the densest packing system, regardless of considering the real physical movements of particles.…”
Section: Introductionmentioning
confidence: 99%
“…i.e., the packing fraction of a saturated random packing for spheres was found to be [ 10 ] and for disks . To obtain a higher packing fraction, an optimized packing approach is often used in modeling the particulate system [ 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 ]; most of these works are based on mathematical modeling of the relations between geometric objects and thus reduce the optimal packing problem to a nonlinear programming problem. However, the objective of this approach is to obtain the densest packing system, regardless of considering the real physical movements of particles.…”
Section: Introductionmentioning
confidence: 99%