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Rods with Misfit and Twisted Ribbons...

ProQuest Information and Learning Co.

Rods with Misfit and Twisted Ribbons : = Two Problems in the Mechanics of Thin Elastic Objects.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Rods with Misfit and Twisted Ribbons :/
Reminder of title:	Two Problems in the Mechanics of Thin Elastic Objects.
Author:	O'Brien, Ethan.
Description:	1 online resource (107 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-12(E), Section: B.
Contained By:	Dissertation Abstracts International78-12B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355128505

Rods with Misfit and Twisted Ribbons : = Two Problems in the Mechanics of Thin Elastic Objects.
O'Brien, Ethan.

Rods with Misfit and Twisted Ribbons :Two Problems in the Mechanics of Thin Elastic Objects. - 1 online resource (107 pages)

Source: Dissertation Abstracts International, Volume: 78-12(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

This thesis addresses two problems in elasticity and the calculus of variations, each of which is outlined below. Both problems involve the minimization of an elastic energy functional with a small parameter; the first is in the area of dimension reduction and Gamma convergence, and the second is an example of energy-driven pattern formation.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355128505Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Rods with Misfit and Twisted Ribbons : = Two Problems in the Mechanics of Thin Elastic Objects.
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020 $a 9780355128505
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035 $a (MiAaPQ)nyu:12943
035 $a AAI10261556
040 $a MiAaPQ $b eng $c MiAaPQ
099 $a TUL $f hyy $c available through World Wide Web
100 1 $a O'Brien, Ethan. $3 1180639
245 1 0 $a Rods with Misfit and Twisted Ribbons : $b Two Problems in the Mechanics of Thin Elastic Objects.
264 0 $c 2017
300 $a 1 online resource (107 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 78-12(E), Section: B.
500 $a Adviser: Robert V. Kohn.
502 $a Thesis (Ph.D.) $c New York University $d 2017.
504 $a Includes bibliographical references
520 $a This thesis addresses two problems in elasticity and the calculus of variations, each of which is outlined below. Both problems involve the minimization of an elastic energy functional with a small parameter; the first is in the area of dimension reduction and Gamma convergence, and the second is an example of energy-driven pattern formation.
520 $a In the first chapter, we derive a one-dimensional variational problem representing the elastic energy of a rod with misfit, starting from a nonlinear, three-dimensional elastic energy with nontrivial preferred strain. Our approach to dimension reduction is to find a small-thickness Gamma-limit. The limiting energy is a quadratic function of the rates at which the rod bends and twists, and we give explicit expressions for the preferred curvature and twist in the special case of isotropic elastic moduli.
520 $a Chapter 2 is motivated by recent experiments by Chopin and Kudrolli [PRL 111:174302, 2013], which showed that a thin elastic ribbon, when twisted into a helicoid, may wrinkle in the center. We seek to explain this. Following the lead of a recent paper by Chopin, Demery, and Davidovitch [J Elasticity 119, 2015, 137-189], we model the ribbon using the framework of elastic energy minimization, starting from a modified von Karman functional. Our main contribution is to show matching upper and lower bounds for the minimum energy in the small-thickness limit. Along the way, we show that the displacements must be small where we expect that the ribbon is helicoidal, and that the ribbon must buckle away from the helicoid in the zone in which we expect wrinkles.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a New York University. $b Mathematics. $3 1180487
773 0 $t Dissertation Abstracts International $g 78-12B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10261556 $z click for full text (PQDT)

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