Introduction To Mathematical Elasticity
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Introduction To Mathematical Elasticity
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Author : Michael J. Cloud
language : en
Publisher: World Scientific
Release Date : 2009
Introduction To Mathematical Elasticity written by Michael J. Cloud and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Science categories.
This book provides the general reader with an introduction to mathematical elasticity, by means of general concepts in classic mechanics, and models for elastic springs, strings, rods, beams and membranes. Functional analysis is also used to explore more general boundary value problems for three-dimensional elastic bodies, where the reader is provided, for each problem considered, a description of the deformation; the equilibrium in terms of stresses; the constitutive equation; the equilibrium equation in terms of displacements; formulation of boundary value problems; and variational principles, generalized solutions and conditions for solvability. Introduction to Mathematical Elasticity will also be of essential reference to engineers specializing in elasticity, and to mathematicians working on abstract formulations of the related boundary value problems. Sample Chapter(s). Foreword (46 KB). Chapter 1: Models and Ideas of Classical Mechanics (634 KB). Contents: Models and Ideas of Classical Mechanics; Simple Elastic Models; Theory of Elasticity: Statics and Dynamics. Readership: Academic and industry: mathematicians, engineers, physicists, students advanced undergraduates in the field of engineering mechanics.
An Introduction To The Mathematical Theory Of Vibrations Of Elastic Plates
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Author : Raymond David Mindlin
language : en
Publisher: World Scientific
Release Date : 2006
An Introduction To The Mathematical Theory Of Vibrations Of Elastic Plates written by Raymond David Mindlin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Technology & Engineering categories.
This book by the late R D Mindlin is destined to become a classic introduction to the mathematical aspects of two-dimensional theories of elastic plates. It systematically derives the two-dimensional theories of anisotropic elastic plates from the variational formulation of the three-dimensional theory of elasticity by power series expansions. The uniqueness of two-dimensional problems is also examined from the variational viewpoint. The accuracy of the two-dimensional equations is judged by comparing the dispersion relations of the waves that the two-dimensional theories can describe with prediction from the three-dimensional theory. Discussing mainly high-frequency dynamic problems, it is also useful in traditional applications in structural engineering as well as provides the theoretical foundation for acoustic wave devices.
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.
Three Dimensional Elasticity
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Author :
language : en
Publisher: Elsevier
Release Date : 1994-01-19
Three Dimensional 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 1994-01-19 with Technology & Engineering categories.
This volume is a thorough introduction to contemporary research in elasticity, and may be used as a working textbook at the graduate level for courses in pure or applied mathematics or in continuum mechanics. It provides a thorough description (with emphasis on the nonlinear aspects) of the two competing mathematical models of three-dimensional elasticity, together with a mathematical analysis of these models. The book is as self-contained as possible.
Introduction To Linear Elasticity
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Author : Phillip L. Gould
language : en
Publisher: Springer
Release Date : 1993-12-09
Introduction To Linear Elasticity written by Phillip L. Gould and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-12-09 with Technology & Engineering categories.
This applications-oriented introduction fills an important gap in the field of solid mechanics. Offering a thorough grounding in the tensor-based theory of elasticity for courses in mechanical, civil, materials or aeronautical engineering, it allows students to apply the basic notions of mechanics to such important topics as stress analysis. Further, they will also acquire the necessary background for more advanced work in elasticity, plasticity, shell theory, composite materials and finite element mechanics. This second edition features new chapters on the bending of thin plates, time-dependent effects, and strength and failure criteria.
Continuum Mechanics And Linear Elasticity
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Author : Ciprian D. Coman
language : en
Publisher: Springer Nature
Release Date : 2019-11-02
Continuum Mechanics And Linear Elasticity written by Ciprian D. Coman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-02 with Technology & Engineering categories.
This is an intermediate book for beginning postgraduate students and junior researchers, and offers up-to-date content on both continuum mechanics and elasticity. The material is self-contained and should provide readers sufficient working knowledge in both areas. Though the focus is primarily on vector and tensor calculus (the so-called coordinate-free approach), the more traditional index notation is used whenever it is deemed more sensible. With the increasing demand for continuum modeling in such diverse areas as mathematical biology and geology, it is imperative to have various approaches to continuum mechanics and elasticity. This book presents these subjects from an applied mathematics perspective. In particular, it extensively uses linear algebra and vector calculus to develop the fundamentals of both subjects in a way that requires minimal use of coordinates (so that beginning graduate students and junior researchers come to appreciate the power of the tensor notation).
An Introduction To The Theory Of Elasticity
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Author : R. J. Atkin
language : en
Publisher: Courier Corporation
Release Date : 2013-02-20
An Introduction To The Theory Of Elasticity written by R. J. Atkin and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-20 with Science categories.
Accessible text covers deformation and stress, derivation of equations of finite elasticity, and formulation of infinitesimal elasticity with application to two- and three-dimensional static problems and elastic waves. 1980 edition.
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].
A Treatise On The Mathematical Theory Of Elasticity
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Author : Augustus Edward Hough Love
language : en
Publisher: Courier Corporation
Release Date : 1944-01-01
A Treatise On The Mathematical Theory Of Elasticity written by Augustus Edward Hough Love and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1944-01-01 with Technology & Engineering categories.
The most complete single-volume treatment of classical elasticity, this text features extensive editorial apparatus, including a historical introduction. Topics include stress, strain, bending, torsion, gravitational effects, and much more. 1927 edition.
Mathematical Theory Of Elastic Structures
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Author : Kang Feng
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Mathematical Theory Of Elastic Structures written by Kang Feng 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 2013-04-17 with Science categories.
Elasticity theory is a classical discipline. The mathematical theory of elasticity in mechanics, especially the linearized theory, is quite mature, and is one of the foundations of several engineering sciences. In the last twenty years, there has been significant progress in several areas closely related to this classical field, this applies in particular to the following two areas. First, progress has been made in numerical methods, especially the development of the finite element method. The finite element method, which was independently created and developed in different ways by sci entists both in China and in the West, is a kind of systematic and modern numerical method for solving partial differential equations, especially el liptic equations. Experience has shown that the finite element method is efficient enough to solve problems in an extremely wide range of applica tions of elastic mechanics. In particular, the finite element method is very suitable for highly complicated problems. One of the authors (Feng) of this book had the good fortune to participate in the work of creating and establishing the theoretical basis of the finite element method. He thought in the early sixties that the method could be used to solve computational problems of solid mechanics by computers. Later practice justified and still continues to justify this point of view. The authors believe that it is now time to include the finite element method as an important part of the content of a textbook of modern elastic mechanics.