An Introduction to Differential Geometry with Applications to Elasticity

An Introduction to Differential Geometry with Applications to Elasticity

English | PDF | 2005 | 212 Pages | ISBN : 1402042477 | 2.27 MB

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].


[Fast Download] An Introduction to Differential Geometry with Applications to Elasticity

Related eBooks:
More Statistical and Methodological Myths and Urban Legends
Scalarization and Separation by Translation Invariant Functions
Dynamical Stabilization of the Fermi Scale
Geometry of Digital Spaces
Applied Categorical and Count Data Analysis
Time Series: Modeling, Computation, and Inference
Handling Qualitative Data, 3rd edition
Lie Algebras, Part 1
Loss Distributions
Spin Glasses: A Challenge for Mathematicians: Cavity and Mean Field Models
Computational Linear and Commutative Algebra
A Brief Introduction to Machine Learning for Engineers
Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.