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001 978-1-4020-4248-5
003 DE-He213
005 20161121231015.0
007 cr nn 008mamaa
008 100301s2005 ne | s |||| 0|eng d
020 _a9781402042485
_9978-1-4020-4248-5
024 7 _a10.1007/1-4020-4248-5
_2doi
050 4 _aTA329-348
050 4 _aTA640-643
072 7 _aTBJ
_2bicssc
072 7 _aMAT003000
_2bisacsh
082 0 4 _a519
_223
100 1 _aCiarlet, Philippe G.
_eauthor.
245 1 3 _aAn Introduction to Differential Geometry with Applications to Elasticity
_h[electronic resource] /
_cby Philippe G. Ciarlet.
264 1 _aDordrecht :
_bSpringer Netherlands,
_c2005.
300 _aVI, 210 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aThree-Dimensional Differential Geometry -- Differential Geometry of Surfaces -- Applications to Three-Dimensional Elasticity in Curvilinear Coordinates -- Applications to Shell Theory.
520 _acurvilinear 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].
650 0 _aEngineering.
650 0 _aPartial differential equations.
650 0 _aDifferential geometry.
650 0 _aMechanics.
650 0 _aApplied mathematics.
650 0 _aEngineering mathematics.
650 1 4 _aEngineering.
650 2 4 _aAppl.Mathematics/Computational Methods of Engineering.
650 2 4 _aMechanics.
650 2 4 _aPartial Differential Equations.
650 2 4 _aDifferential Geometry.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781402042478
856 4 0 _uhttp://dx.doi.org/10.1007/1-4020-4248-5
912 _aZDB-2-ENG
950 _aEngineering (Springer-11647)
999 _c507194
_d507194