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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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An Introduction to Differential Geometry with Applications to Elasticity (Paperback, Softcover reprint of hardcover 1st ed. 2005)
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An Introduction to Differential Geometry with Applications to Elasticity (Paperback, Softcover reprint of hardcover 1st ed. 2005)
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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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