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.
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.
An Introduction To Differential Geometry With Applications To Elasticity
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Author : Philippe G. Ciarlet
language : en
Publisher:
Release Date : 2005
An Introduction To Differential Geometry With Applications To Elasticity written by Philippe G. Ciarlet and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
Mathematical Foundations Of Elasticity
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Author : Jerrold E. Marsden
language : en
Publisher: Courier Corporation
Release Date : 1994-01-01
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 1994-01-01 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.
Elasticity Theory And Applications
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Author : Adel S. Saada
language : en
Publisher: Krieger Publishing Company
Release Date : 1993
Elasticity Theory And Applications written by Adel S. Saada and has been published by Krieger Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Science categories.
This work, intended to be of use to advanced undergraduates and graduates, provides a foundation for training in advanced elasticity, plasticity, fracture, elastic stability, plates and shells. Emphasis is placed on geometry, and the concept of tensor and its associated notations is introduced.
Treatise On Classical Elasticity
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Author : Petre P. Teodorescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-07-08
Treatise On Classical Elasticity written by Petre P. Teodorescu 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 2014-07-08 with Science categories.
Deformable solids have a particularly complex character; mathematical modeling is not always simple and often leads to inextricable difficulties of computation. One of the simplest mathematical models and, at the same time, the most used model, is that of the elastic body – especially the linear one. But, notwithstanding its simplicity, even this model of a real body may lead to great difficulties of computation. The practical importance of a work about the theory of elasticity, which is also an introduction to the mechanics of deformable solids, consists of the use of scientific methods of computation in a domain in which simplified methods are still used. This treatise takes into account the consideration made above, with special attention to the theoretical study of the state of strain and stress of a deformable solid. The book draws on the known specialized literature, as well as the original results of the author and his 50+ years experience as Professor of Mechanics and Elasticity at the University of Bucharest. The construction of mathematical models is made by treating geometry and kinematics of deformation, mechanics of stresses and constitutive laws. Elastic, plastic and viscous properties are thus put in evidence and the corresponding theories are developed. Space problems are treated and various particular cases are taken into consideration. New solutions for boundary value problems of finite and infinite domains are given and a general theory of concentrated loads is built. Anisotropic and non-homogeneous bodies are studied as well. Cosserat type bodies are also modeled. The connection with thermal and viscous phenomena will be considered too. Audience: researchers in applied mathematics, mechanical and civil engineering.
Geometrical Foundations Of Continuum Mechanics
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Author : Paul Steinmann
language : en
Publisher: Springer
Release Date : 2015-03-25
Geometrical Foundations Of Continuum Mechanics written by Paul Steinmann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-25 with Science categories.
This book illustrates the deep roots of the geometrically nonlinear kinematics of generalized continuum mechanics in differential geometry. Besides applications to first- order elasticity and elasto-plasticity an appreciation thereof is particularly illuminating for generalized models of continuum mechanics such as second-order (gradient-type) elasticity and elasto-plasticity. After a motivation that arises from considering geometrically linear first- and second- order crystal plasticity in Part I several concepts from differential geometry, relevant for what follows, such as connection, parallel transport, torsion, curvature, and metric for holonomic and anholonomic coordinate transformations are reiterated in Part II. Then, in Part III, the kinematics of geometrically nonlinear continuum mechanics are considered. There various concepts of differential geometry, in particular aspects related to compatibility, are generically applied to the kinematics of first- and second- order geometrically nonlinear continuum mechanics. Together with the discussion on the integrability conditions for the distortions and double-distortions, the concepts of dislocation, disclination and point-defect density tensors are introduced. For concreteness, after touching on nonlinear fir st- and second-order elasticity, a detailed discussion of the kinematics of (multiplicative) first- and second-order elasto-plasticity is given. The discussion naturally culminates in a comprehensive set of different types of dislocation, disclination and point-defect density tensors. It is argued, that these can potentially be used to model densities of geometrically necessary defects and the accompanying hardening in crystalline materials. Eventually Part IV summarizes the above findings on integrability whereby distinction is made between the straightforward conditions for the distortion and the double-distortion being integrable and the more involved conditions for the strain (metric) and the double-strain (connection) being integrable. The book addresses readers with an interest in continuum modelling of solids from engineering and the sciences alike, whereby a sound knowledge of tensor calculus and continuum mechanics is required as a prerequisite.
Mathematical Elasticity
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Author :
language : en
Publisher: Elsevier
Release Date : 1997-07-22
Mathematical Elasticity written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-07-22 with Mathematics categories.
The objective of Volume II is to show how asymptotic methods, with the thickness as the small parameter, indeed provide a powerful means of justifying two-dimensional plate theories. More specifically, without any recourse to any a priori assumptions of a geometrical or mechanical nature, it is shown that in the linear case, the three-dimensional displacements, once properly scaled, converge in H1 towards a limit that satisfies the well-known two-dimensional equations of the linear Kirchhoff-Love theory; the convergence of stress is also established. In the nonlinear case, again after ad hoc scalings have been performed, it is shown that the leading term of a formal asymptotic expansion of the three-dimensional solution satisfies well-known two-dimensional equations, such as those of the nonlinear Kirchhoff-Love theory, or the von Kármán equations. Special attention is also given to the first convergence result obtained in this case, which leads to two-dimensional large deformation, frame-indifferent, nonlinear membrane theories. It is also demonstrated that asymptotic methods can likewise be used for justifying other lower-dimensional equations of elastic shallow shells, and the coupled pluri-dimensional equations of elastic multi-structures, i.e., structures with junctions. In each case, the existence, uniqueness or multiplicity, and regularity of solutions to the limit equations obtained in this fashion are also studied.
Calculus Of Variations On Thin Prestressed Films
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Author : Marta Lewicka
language : en
Publisher: Springer Nature
Release Date : 2023-04-17
Calculus Of Variations On Thin Prestressed Films written by Marta Lewicka and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-17 with Mathematics categories.
This monograph considers the analytical and geometrical questions emerging from the study of thin elastic films that exhibit residual stress at free equilibria. It provides the comprehensive account, the details and background on the most recent results in the combined research perspective on the classical themes: in Differential Geometry – that of isometrically embedding a shape with a given metric in an ambient space of possibly different dimension, and in Calculus of Variations – that of minimizing non-convex energy functionals parametrized by a quantity in whose limit the functionals become degenerate. Prestressed thin films are present in many contexts and applications, such as: growing tissues, plastically strained sheets, engineered swelling or shrinking gels, petals and leaves of flowers, or atomically thin graphene layers. While the related questions about the physical basis for shape formation lie at the intersection of biology, chemistry and physics, fundamentally they are of the analytical and geometrical character, and can be tackled using the techniques of the dimension reduction, laid out in this book. The text will appeal to mathematicians and graduate students working in the fields of Analysis, Calculus of Variations, Partial Differential Equations, and Applied Math. It will also be of interest to researchers and graduate students in Engineering (especially fields related to Solid Mechanics and Materials Science), who would like to gain the modern mathematical insight and learn the necessary tools.