000 | 03468nam a22005055i 4500 | ||
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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 |
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024 | 7 |
_a10.1007/1-4020-4248-5 _2doi |
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050 | 4 | _aTA329-348 | |
050 | 4 | _aTA640-643 | |
072 | 7 |
_aTBJ _2bicssc |
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072 | 7 |
_aMAT003000 _2bisacsh |
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082 | 0 | 4 |
_a519 _223 |
100 | 1 |
_aCiarlet, Philippe G. _eauthor. |
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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. |
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300 |
_aVI, 210 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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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 |