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An Introduction to Differential Geometry with Applications to Elasticity

  • Book
  • © 2005

Overview

Authors:
  1. Philippe G. Ciarlet

    1. City University of Hong Kong, Hong Kong

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  • Self-contained treatment
  • Interplay between differential geometry and elasticity theory

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-2
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  2. Three-Dimensional Differential Geometry

    Pages 3-52

  3. Differential Geometry of Surfaces

    Pages 53-102

  4. Applications to Three-Dimensional Elasticity in Curvilinear Coordinates

    Pages 103-145

  5. Applications to Shell Theory

    Pages 147-193

  6. Back Matter

    Pages 195-209
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Keywords

About this book

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].

Reviews

From the reviews:

"This is a book about differential geometry and elasticity theory also published earlier as journal article. And, indeed it covers both subjects in a coextensive way that can not be found in any other book in the field. … the list of references containing more than 120 items is representative enough and the interested reader should be able to find them among these." (Ivailo Mladenov, Zentralblatt MATH, Vol. 1100 (2), 2007)

Authors and Affiliations

  • City University of Hong Kong, Hong Kong

    Philippe G. Ciarlet

Bibliographic Information

  • Book Title: An Introduction to Differential Geometry with Applications to Elasticity

  • Authors: Philippe G. Ciarlet

  • DOI: https://doi.org/10.1007/1-4020-4248-5

  • Publisher: Springer Dordrecht

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer Science+Business Media B.V. 2005

  • Hardcover ISBN: 978-1-4020-4247-8Published: 22 February 2006

  • Softcover ISBN: 978-90-481-7085-2Published: 19 October 2010

  • eBook ISBN: 978-1-4020-4248-5Published: 28 June 2006

  • Edition Number: 1

  • Number of Pages: VI, 209

  • Additional Information: Reprinted from Journal of Elasticity, Vol 78-79 (2005)

  • Topics: Mathematical and Computational Engineering, Classical Mechanics, Partial Differential Equations, Differential Geometry

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