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An Introduction to Differential Geometry with Applications to Elasticity - pocketboek

2010

ISBN: 9789048170852

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An Introduction to Differential Geometry with Applications to Elasticity - pocketboek

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An Introduction to Differential Geometry with Applications to Elasticity

This monograph presents the basic theorems of differential geometry in three-dimensional space, including a thorough coverage of surface theory. By means of a series of carefully selected and representative mathematical models this monograph also explains at length how these theorems are used in three-dimensional elasticity and in shell theory. The presentation is essentially selfcontained, with a great emphasis on pedagogy. In particular, no "a priori" knowledge of differential geometry or of elasticity theory is assumed, the only requirements are a reasonable knowledge of basic analysis, functional analysis, and some acquaintance with ordinary and partial differential equations.

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EAN (ISBN-13): 9789048170852
ISBN (ISBN-10): 9048170850
Gebonden uitgave
pocket book
Verschijningsjaar: 2010
Uitgever: Springer
216 Bladzijden
Gewicht: 0,352 kg
Taal: eng/Englisch

Boek bevindt zich in het datenbestand sinds 2010-04-29T12:27:19+02:00 (Amsterdam)
Detailpagina laatst gewijzigd op 2022-07-17T17:27:23+02:00 (Amsterdam)
ISBN/EAN: 9789048170852

ISBN - alternatieve schrijfwijzen:
90-481-7085-0, 978-90-481-7085-2


Gegevens van de uitgever

Auteur: Philippe G. Ciarlet
Titel: An Introduction to Differential Geometry with Applications to Elasticity
Uitgeverij: Springer; Springer Netherland
210 Bladzijden
Verschijningsjaar: 2010-10-19
Dordrecht; NL
Gedrukt / Gemaakt in
Gewicht: 0,454 kg
Taal: Engels
160,49 € (DE)
164,99 € (AT)
177,00 CHF (CH)
POD
VI, 210 p.

BC; Previously published in hardcover; Hardcover, Softcover / Technik/Allgemeines, Lexika; Mathematik für Ingenieure; Verstehen; Gaussian curvature; curvature; curvilinear coordinates; differential geometry; differential geometry of surfaces; elasticity theory; shell theory; surface theory; partial differential equations; B; Mathematical and Computational Engineering; Classical Mechanics; Partial Differential Equations; Differential Geometry; Mathematical and Computational Engineering Applications; Classical Mechanics; Differential Equations; Differential Geometry; Engineering; Klassische Mechanik; Differentialrechnung und -gleichungen; Differentielle und Riemannsche Geometrie; BB

Preface; Chapter 1. Three-dimensional differential geometry: 1.1. Curvilinear coordinates, 1.2. Metric tensor, 1.3. Volume, areas, and lengths in curvilinear coordinates, 1.4. Covariant derivatives of a vector field, 1.5. Necessary conditions satisfied by the metric tensor; the Riemann curvature tensor, 1.6. Existence of an immersion defined on an open set in R3 with a prescribed metric tensor, 1.7. Uniqueness up to isometries of immersions with the same metric tensor, 1.8. Continuity of an immersion as a function of its metric tensor; Chapter 2. Differential geometry of surfaces: 2.1. Curvilinear coordinates on a surface, 2.2. First fundamental form, 2.3. Areas and lengths on a surface, 2.4. Second fundamental form; curvature on a surface, 2.5. Principal curvatures; Gaussian curvature, 2.6. Covariant derivatives of a vector field defined on a surface; the Gauss and Weingarten formulas, 2.7. Necessary conditions satisfied by the first and second fundamental forms: the Gauss and Codazzi-Mainardi equations; Gauss' theorema egregium, 2.8. Existence of a surface with prescribed first and second fundamental forms, 2.9. Uniqueness up to proper isometries of surfaces with the same fundamental forms, 2.10.Continuity of a surface as a function of its fundamental forms; Chapter 3. Applications to three-dimensional elasticity in curvilinear coordinates: 3.1. The equations of nonlinear elasticity in Cartesian coordinates, 3.2. Principle of virtual work in curvilinear coordinates, 3.3. Equations of equilibrium in curvilinear coordinates; covariant derivatives of a tensor field, 3.4. Constitutive equation in curvilinear coordinates, 3.5. The equations of nonlinear elasticity in curvilinear coordinates, 3.6. The equations of linearized elasticity in curvilinear coordinates, 3.7. A fundamental lemma of J.L. Lions, 3.8. Korn's inequalities in curvilinear coordinates, 3.9. Existence and uniqueness theorems in linearizedelasticity in curvilinear coordinates; Chapter 4. Applications to shell theory: 4.1. The nonlinear Koiter shell equations, 4.2. The linear Koiter shell equations, 4.3. Korn’s inequality on a surface, 4.4. Existence and uniqueness theorems for the linear Koiter shell equations; covariant derivatives of a tensor field defined on a surface, 4.5. A brief review of linear shell theories; References; Index.

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