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Synopsis
curvilinear coordinates. This treatment includes in particular a direct proof of the three-dimensional Korn inequality in curvilinear coordinates. The fourth and last chapter, which heavily relies on Chapter 2, begins by a detailed description of the nonlinear and linear equations proposed by W.T. Koiter for modeling thin elastic shells. These equations are "two-dimensional", in the sense that they are expressed in terms of two curvilinear coordinates used for de?ning the middle surface of the shell. The existence, uniqueness, and regularity of solutions to the linear Koiter equations is then established, thanks this time to a fundamental "Korn inequality on a surface" and to an "in?nit- imal rigid displacement lemma on a surface". This chapter also includes a brief introduction to other two-dimensional shell equations. Interestingly, notions that pertain to di?erential geometry per se, suchas covariant derivatives of tensor ?elds, are also introduced in Chapters 3 and 4, where they appear most naturally in the derivation of the basic boundary value problems of three-dimensional elasticity and shell theory. Occasionally, portions of the material covered here are adapted from - cerpts from my book "Mathematical Elasticity, Volume III: Theory of Shells", published in 2000by North-Holland, Amsterdam; in this respect, I am indebted to Arjen Sevenster for his kind permission to rely on such excerpts. Oth- wise, the bulk of this work was substantially supported by two grants from the Research Grants Council of Hong Kong Special Administrative Region, China [Project No. 9040869, CityU 100803 and Project No. 9040966, CityU 100604].
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An Introduction to Differential Geometry with Applications to Elasticity
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An Introduction to Differential Geometry with Applications to Elasticity.
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Berlin : Springer Netherland, 2005
ISBN 10 : 1402042477
ISBN 13 : 9781402042478
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An Introduction to Differential Geometry with Applications to Elasticity
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An Introduction to Differential Geometry with Applications to Elasticity
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An Introduction to Differential Geometry with Applications to Elasticity
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Springer Netherlands Feb 2006, 2006
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ISBN 13 : 9781402042478
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Buch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -curvilinear coordinates. This treatment includes in particular a direct proof of the three-dimensional Korn inequality in curvilinear coordinates. The fourth and last chapter, which heavily relies on Chapter 2, begins by a detailed description of the nonlinear and linear equations proposed by W.T. Koiter for modeling thin elastic shells. These equations are 'two-dimensional', in the sense that they are expressed in terms of two curvilinear coordinates used for de ning the middle surface of the shell. The existence, uniqueness, and regularity of solutions to the linear Koiter equations is then established, thanks this time to a fundamental 'Korn inequality on a surface' and to an 'in nit- imal rigid displacement lemma on a surface'. This chapter also includes a brief introduction to other two-dimensional shell equations. Interestingly, notions that pertain to di erential geometry per se,suchas covariant derivatives of tensor elds, are also introduced in Chapters 3 and 4, where they appear most naturally in the derivation of the basic boundary value problems of three-dimensional elasticity and shell theory. Occasionally, portions of the material covered here are adapted from - cerpts from my book 'Mathematical Elasticity, Volume III: Theory of Shells', published in 2000by North-Holland, Amsterdam; in this respect, I am indebted to Arjen Sevenster for his kind permission to rely on such excerpts. Oth- wise, the bulk of this work was substantially supported by two grants from the Research Grants Council of Hong Kong Special Administrative Region, China [Project No. 9040869, CityU 100803 and Project No. 9040966, CityU 100604]. 216 pp. Englisch. N° de réf. du vendeur 9781402042478
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An Introduction to Differential Geometry with Applications to Elasticity
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Introduction to Differential Geometry With Applications to Elasticity
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Introduction to Differential Geometry With Applications to Elasticity
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An Introduction to Differential Geometry with Applications to Elasticity
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Springer Netherlands, 2006
ISBN 10 : 1402042477
ISBN 13 : 9781402042478
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Gebunden. Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Complete proofsSelf-contained treatmentInterplay between differential geometry and elasticity theorycurvilinear coordinates. This treatment includes in particular a direct proof of the three-dimensional Korn inequality in curvilinea. N° de réf. du vendeur 4093676
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An Introduction to Differential Geometry with Applications to Elasticity
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An Introduction to Differential Geometry with Applications to Elasticity
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Buch. Etat : Neu. This item is printed on demand - Print on Demand Titel. Neuware -curvilinear coordinates. This treatment includes in particular a direct proof of the three-dimensional Korn inequality in curvilinear coordinates. The fourth and last chapter, which heavily relies on Chapter 2, begins by a detailed description of the nonlinear and linear equations proposed by W.T. Koiter for modeling thin elastic shells. These equations are ¿two-dimensional¿, in the sense that they are expressed in terms of two curvilinear coordinates used for de ning the middle surface of the shell. The existence, uniqueness, and regularity of solutions to the linear Koiter equations is then established, thanks this time to a fundamental ¿Korn inequality on a surface¿ and to an ¿in nit- imal rigid displacement lemma on a surface¿. This chapter also includes a brief introduction to other two-dimensional shell equations. Interestingly, notions that pertain to di erential geometry per se,suchas covariant derivatives of tensor elds, are also introduced in Chapters 3 and 4, where they appear most naturally in the derivation of the basic boundary value problems of three-dimensional elasticity and shell theory. Occasionally, portions of the material covered here are adapted from - cerpts from my book ¿Mathematical Elasticity, Volume III: Theory of Shells¿, published in 2000by North-Holland, Amsterdam; in this respect, I am indebted to Arjen Sevenster for his kind permission to rely on such excerpts. Oth- wise, the bulk of this work was substantially supported by two grants from the Research Grants Council of Hong Kong Special Administrative Region, China [Project No. 9040869, CityU 100803 and Project No. 9040966, CityU 100604].Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 216 pp. Englisch. N° de réf. du vendeur 9781402042478
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