NDLI: Optimal placements of flexible objects. I. Analytical results for the unbounded case

Content Provider	IEEE Xplore Digital Library
Author	Albrecht, A. Cheung, S.K. Hui, K.C. Leung, K.S. Wong, C.K.
Copyright Year	1968
Abstract	The authors consider optimal placements of two-dimensional flexible (elastic, deformable) objects. The objects are discs of equal size placed within a rigid boundary. The paper is divided into two parts. In the first part, analytical results for three types of regular, periodic arrangements-the hexagonal, square, and triangular placements-are presented. The regular arrangements are analyzed for rectangular boundaries and radii of discs that are small compared to the area of the placement region, because, in this case, the influence of boundary conditions can be neglected. This situation is called the unbounded case. They show that, for the unbounded case among the three regular placements, the type of hexagonal arrangements provides the largest number of placed units for the same deformation depth. Furthermore, it can be proved that these regular placements are not too far from the truly optimal arrangements. For example, hexagonal placements differ at most by the factor of 1.1 from the largest possible number of generally shaped units in arbitrary arrangements. These analytical results are used as guidances for testing stochastic algorithms optimizing placements of flexible objects. In the second part, mainly two problems are considered: the underlying physical model and a simulated annealing algorithm maximizing the number of flexible discs in equilibrium placements. Along with the physical model, an approximate formula is derived, reflecting the deformation/force relationship for a large range of deformations.
Sponsorship	IEEE Computer Society Technical Committee on Distributed Process IEEE Computer Society Technical Committee on VLSI IEEE Technical Committee on Computer Architecture IEEE Computer Society
Starting Page	890
Ending Page	904
Page Count	15
File Size	235376
File Format	PDF
ISSN	00189340
Volume Number	46
Issue Number	8
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1997-08-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Computer aided software engineering Algorithm design and analysis Stochastic processes Simulated annealing Shape Elasticity Boundary conditions Testing Deformable models Amorphous materials
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Computational Theory and Mathematics Software Hardware and Architecture

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