An Introduction to Differential Geometry with Applications to Elasticity

Philippe G. Ciarlet

ISBN 10: 9048170850 / ISBN 13: 9789048170852

Published by Springer Netherland, 2010

About this Item

An Introduction to Differential Geometry with Applications to Elasticity | Philippe G. Ciarlet | Taschenbuch | vi | Englisch | 2010 | Springer Netherland | EAN 9789048170852 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.

Seller Inventory # 107119768

Bibliographic Details

• Title: An Introduction to Differential Geometry with Applications to Elasticity
• Publisher: Springer Netherland
• Publication Date: 2010
• Language: English
• ISBN 10: 9048170850
• ISBN 13: 9789048170852
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 240W x 160H x 12D millimeters 240 millimeters width by 160 millimeters height by 12 millimeters depth
• Weight: 354 grams
• Seller catalogs:
  • Bücher

About this title

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].

Review

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)