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Topics in the mathematical theory of nonlinear elasticity.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Topics in the mathematical theory of nonlinear elasticity./
Author:	Li, Hui.
Description:	1 online resource (129 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 74-04, Section: B.
Contained By:	Dissertations Abstracts International74-04B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3540924click for full text (PQDT)
ISBN:	9781267667434

Topics in the mathematical theory of nonlinear elasticity.
Li, Hui.

Topics in the mathematical theory of nonlinear elasticity. - 1 online resource (129 pages)

Source: Dissertations Abstracts International, Volume: 74-04, Section: B.

Thesis (Ph.D.)--University of Minnesota, 2012.

Includes bibliographical references

My thesis consists of two interrelated parts. The first part lies in the field of the mathematical theory of nonlinear elasticity, and it concerns the rigorous derivation of theories for elastic shells. The second part concerns modeling and analyzing of shells with residual stresses. The approach for both parts is based on the refined methods in Calculus of Variations (notably the so-called Γ-convergence) and a combination of the arguments in modern Mathematical Analysis and Riemannian Geometry. More precisely, in chapter 2-3, we derive the von Karman theory for variable thickness shells and also the von Karman theory for incompressible shells with uniform thickness. In chapter 4-5, we first establish the Kirchhoff theory for non-Euclidean shells and its incompressible counterpart. Then, we also derive the incompatible Foppl-von Karman theory for prestrained shells with variable thickness, calculate the associated Euler-Lagrange equations and found the convergence of equilibria. Finally, the incompatible Foppl-von Karman theory for incompressible prestrained shells and the associated Euler-Lagrange equations are investigated.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9781267667434Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Calculus of variationsIndex Terms--Genre/Form:

542853
Electronic books.

Topics in the mathematical theory of nonlinear elasticity.
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245 1 0 $a Topics in the mathematical theory of nonlinear elasticity.
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500 $a Source: Dissertations Abstracts International, Volume: 74-04, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Lewicka, Marta.
502 $a Thesis (Ph.D.)--University of Minnesota, 2012.
504 $a Includes bibliographical references
520 $a My thesis consists of two interrelated parts. The first part lies in the field of the mathematical theory of nonlinear elasticity, and it concerns the rigorous derivation of theories for elastic shells. The second part concerns modeling and analyzing of shells with residual stresses. The approach for both parts is based on the refined methods in Calculus of Variations (notably the so-called Γ-convergence) and a combination of the arguments in modern Mathematical Analysis and Riemannian Geometry. More precisely, in chapter 2-3, we derive the von Karman theory for variable thickness shells and also the von Karman theory for incompressible shells with uniform thickness. In chapter 4-5, we first establish the Kirchhoff theory for non-Euclidean shells and its incompressible counterpart. Then, we also derive the incompatible Foppl-von Karman theory for prestrained shells with variable thickness, calculate the associated Euler-Lagrange equations and found the convergence of equilibria. Finally, the incompatible Foppl-von Karman theory for incompressible prestrained shells and the associated Euler-Lagrange equations are investigated.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2023
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 515831
650 4 $a Applied mathematics. $3 2122814
653 $a Calculus of variations
653 $a Gamma-convergence
653 $a Nonlinear elasticity
655 7 $a Electronic books. $2 lcsh $3 542853
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773 0 $t Dissertations Abstracts International $g 74-04B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3540924 $z click for full text (PQDT)