An Introduction to Differential Geometry with Applications to Elasticity

An Introduction to Differential Geometry with Applications to Elasticity
Title An Introduction to Differential Geometry with Applications to Elasticity PDF eBook
Author Philippe G. Ciarlet
Publisher Springer Science & Business Media
Pages 212
Release 2006-06-28
Genre Technology & Engineering
ISBN 1402042485

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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].

An Introduction to Differential Geometry with Applications to Elasticity

An Introduction to Differential Geometry with Applications to Elasticity
Title An Introduction to Differential Geometry with Applications to Elasticity PDF eBook
Author Philippe G. Ciarlet
Publisher
Pages 220
Release 2005
Genre
ISBN

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Introduction to Numerical Linear Algebra and Optimisation

Introduction to Numerical Linear Algebra and Optimisation
Title Introduction to Numerical Linear Algebra and Optimisation PDF eBook
Author Philippe G. Ciarlet
Publisher Cambridge University Press
Pages 456
Release 1989-08-25
Genre Computers
ISBN 9780521339841

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The purpose of this book is to give a thorough introduction to the most commonly used methods of numerical linear algebra and optimisation. The prerequisites are some familiarity with the basic properties of matrices, finite-dimensional vector spaces, advanced calculus, and some elementary notations from functional analysis. The book is in two parts. The first deals with numerical linear algebra (review of matrix theory, direct and iterative methods for solving linear systems, calculation of eigenvalues and eigenvectors) and the second, optimisation (general algorithms, linear and nonlinear programming). The author has based the book on courses taught for advanced undergraduate and beginning graduate students and the result is a well-organised and lucid exposition. Summaries of basic mathematics are provided, proofs of theorems are complete yet kept as simple as possible, and applications from physics and mechanics are discussed. Professor Ciarlet has also helpfully provided over 40 line diagrams, a great many applications, and a useful guide to further reading. This excellent textbook, which is translated and revised from the very successful French edition, will be of great value to students of numerical analysis, applied mathematics and engineering.

Differential Geometry

Differential Geometry
Title Differential Geometry PDF eBook
Author Ta-tsien Li
Publisher World Scientific
Pages 302
Release 2008
Genre Mathematics
ISBN 9812771476

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This book gives the basic notions of differential geometry, such as the metric tensor, the Riemann curvature tensor, the fundamental forms of a surface, covariant derivatives, and the fundamental theorem of surface theory in a self-contained and accessible manner. Although the field is often considered a OC classicalOCO one, it has recently been rejuvenated, thanks to the manifold applications where it plays an essential role.The book presents some important applications to shells, such as the theory of linearly and nonlinearly elastic shells, the implementation of numerical methods for shells, and mesh generation in finite element methods.This volume will be very useful to graduate students and researchers in pure and applied mathematics."

Mathematical Foundations of Elasticity

Mathematical Foundations of Elasticity
Title Mathematical Foundations of Elasticity PDF eBook
Author Jerrold E. Marsden
Publisher Courier Corporation
Pages 578
Release 2012-10-25
Genre Technology & Engineering
ISBN 0486142272

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Graduate-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It presents a classical subject in a modern setting, with examples of newer mathematical contributions. 1983 edition.

Inequalities for Differential Forms

Inequalities for Differential Forms
Title Inequalities for Differential Forms PDF eBook
Author Ravi P. Agarwal
Publisher Springer Science & Business Media
Pages 392
Release 2009-09-19
Genre Mathematics
ISBN 0387684174

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This monograph is the first one to systematically present a series of local and global estimates and inequalities for differential forms, in particular the ones that satisfy the A-harmonic equations. The presentation focuses on the Hardy-Littlewood, Poincare, Cacciooli, imbedded and reverse Holder inequalities. Integral estimates for operators, such as homotopy operator, the Laplace-Beltrami operator, and the gradient operator are discussed next. Additionally, some related topics such as BMO inequalities, Lipschitz classes, Orlicz spaces and inequalities in Carnot groups are discussed in the concluding chapter. An abundance of bibliographical references and historical material supplement the text throughout. This rigorous presentation requires a familiarity with topics such as differential forms, topology and Sobolev space theory. It will serve as an invaluable reference for researchers, instructors and graduate students in analysis and partial differential equations and could be used as additional material for specific courses in these fields.

Tensors, Differential Forms, and Variational Principles

Tensors, Differential Forms, and Variational Principles
Title Tensors, Differential Forms, and Variational Principles PDF eBook
Author David Lovelock
Publisher Courier Corporation
Pages 402
Release 2012-04-20
Genre Mathematics
ISBN 048613198X

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Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.