Elasticity And Geometry

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Elasticity And Geometry

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Author : Basile Audoly
language : en
Publisher: Oxford University Press
Release Date : 2010-06-24

Elasticity And Geometry written by Basile Audoly and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-24 with Mathematics categories.

We experience elasticity everywhere in everyday life. This book covers several modern aspects of the established field of elasticity theory, applying general methods of classical analysis including advanced nonlinear aspects to derive detailed solutions to specific problems. It can serve as an introduction to nonlinear methods in science.

Elasticity And Geometry

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Author : Basile Audoly
language : en
Publisher: OUP Oxford
Release Date : 2010-06-24

Elasticity And Geometry written by Basile Audoly and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-24 with Science categories.

We experience elasticity everywhere in everyday life. This book covers several modern aspects of the established field of elasticity theory, applying general methods of classical analysis including advanced nonlinear aspects to derive detailed solutions to specific problems. It can serve as an introduction to nonlinear methods in science.

Elasticity And Geometry

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Author : Basile Audoly
language : en
Publisher: OUP Oxford
Release Date : 2010-06-24

Elasticity And Geometry written by Basile Audoly and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-24 with Science categories.

We experience elasticity everywhere in daily life: in the straightening or curling of hairs, the irreversible deformations of car bodies after a crash, or the bouncing of elastic balls in ping-pong or soccer. The theory of elasticity is essential to the recent developments of applied and fundamental science, such as the bio-mechanics of DNA filaments and other macro-molecules, and the animation of virtual characters in computer graphics and materials science. In this book, the emphasis is on the elasticity of thin bodies (plates, shells, rods) in connection with geometry. It covers such topics as the mechanics of hairs (curled and straight), the buckling instabilities of stressed plates, including folds and conical points appearing at larger stresses, the geometric rigidity of elastic shells, and the delamination of thin compressed films. It applies general methods of classical analysis, including advanced nonlinear aspects (bifurcation theory, boundary layer analysis), to derive detailed, fully explicit solutions to specific problems. These theoretical concepts are discussed in connection with experiments. Mathematical prerequisites are vector analysis and differential equations. The book can serve as a concrete introduction to nonlinear methods in analysis.

An Introduction To Differential Geometry With Applications To Elasticity

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Author : Philippe G. Ciarlet
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-28

An Introduction To Differential Geometry With Applications To Elasticity written by Philippe G. Ciarlet and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-28 with Technology & Engineering categories.

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].

Mathematical Foundations Of Elasticity

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Author : Jerrold E. Marsden
language : en
Publisher: Courier Corporation
Release Date : 2012-10-25

Mathematical Foundations Of Elasticity written by Jerrold E. Marsden and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-25 with Technology & Engineering categories.

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.

Introduction To Numerical Linear Algebra And Optimisation

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Author : Philippe G. Ciarlet
language : en
Publisher: Cambridge University Press
Release Date : 1989-08-25

Introduction To Numerical Linear Algebra And Optimisation written by Philippe G. Ciarlet and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-08-25 with Computers categories.

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.

Geometric Methods In The Elastic Theory Of Membranes In Liquid Crystal Phases

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Author : Zhong-Can Ou-Yang
language : en
Publisher: World Scientific
Release Date : 1999

Geometric Methods In The Elastic Theory Of Membranes In Liquid Crystal Phases written by Zhong-Can Ou-Yang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Science categories.

This book contains a comprehensive description of the mechanical equilibrium and deformation of membranes as a surface problem in differential geometry. Following the pioneering work by W Helfrich, the fluid membrane is seen as a nematic or smectic ? A liquid crystal film and its elastic energy form is deduced exactly from the curvature elastic theory of the liquid crystals. With surface variation the minimization of the energy at fixed osmotical pressure and surface tension gives a completely new surface equation in geometry that involves potential interest in mathematics. The investigations of the rigorous solution of the equation that have been carried out in recent years by the authors and their co-workers are presented here, among which the torus and the discocyte (the normal shape of the human red blood cell) may attract attention in cell biology. Within the framework of our mathematical model by analogy with cholesteric liquid crystals, an extensive investigation is made of the formation of the helical structures in a tilted chiral lipid bilayer, which has now become a hot topic in the fields of soft matter and biomembranes.

Elasticity And Plasticity

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Author : J. N. Goodier
language : en
Publisher: Courier Dover Publications
Release Date : 2016-04-21

Elasticity And Plasticity written by J. N. Goodier and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-21 with Mathematics categories.

Comprising two classic essays by experts on the mathematical theories of elasticity and plasticity, this volume is noteworthy for its contributions by Russian authors and others previously unrecognized in Western literature. 1958 edition.

Differential Geometry And Continuum Mechanics

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Author : Gui-Qiang G. Chen
language : en
Publisher: Springer
Release Date : 2015-08-11

Differential Geometry And Continuum Mechanics written by Gui-Qiang G. Chen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-11 with Mathematics categories.

This book examines the exciting interface between differential geometry and continuum mechanics, now recognised as being of increasing technological significance. Topics discussed include isometric embeddings in differential geometry and the relation with microstructure in nonlinear elasticity, the use of manifolds in the description of microstructure in continuum mechanics, experimental measurement of microstructure, defects, dislocations, surface energies, and nematic liquid crystals. Compensated compactness in partial differential equations is also treated. The volume is intended for specialists and non-specialists in pure and applied geometry, continuum mechanics, theoretical physics, materials and engineering sciences, and partial differential equations. It will also be of interest to postdoctoral scientists and advanced postgraduate research students. These proceedings include revised written versions of the majority of papers presented by leading experts at the ICMS Edinburgh Workshop on Differential Geometry and Continuum Mechanics held in June 2013. All papers have been peer reviewed.

Topics In Finite Elasticity

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Author : Morton E. Gurtin
language : en
Publisher: SIAM
Release Date : 1981-01-01

Topics In Finite Elasticity written by Morton E. Gurtin and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-01-01 with Technology & Engineering categories.

Finite elasticity is a theory of elastic materials that are capable of undergoing large deformations. This theory is inherently nonlinear and is mathematically quite complex. This monograph presents a derivation of the basic equations of the theory, a discussion of the general boundary-value problems, and a treatment of several interesting and important special topics such as simple shear, uniqueness, the tensile deformations of a cube, and antiplane shear. The monograph is intended for engineers, physicists, and mathematicians.