Introduction to Mathematical Elasticity

Introduction to Mathematical Elasticity

Author: L. P. Lebedev

Publisher: World Scientific

Published: 2009

Total Pages: 317

ISBN-13: 9814273724

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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.


Book Synopsis Introduction to Mathematical Elasticity by : L. P. Lebedev

Download or read book Introduction to Mathematical Elasticity written by L. P. Lebedev and published by World Scientific. This book was released on 2009 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Introduction To Mathematical Elasticity

Introduction To Mathematical Elasticity

Author: Leonid P Lebedev

Publisher: World Scientific

Published: 2009-09-03

Total Pages: 317

ISBN-13: 9814467790

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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.


Book Synopsis Introduction To Mathematical Elasticity by : Leonid P Lebedev

Download or read book Introduction To Mathematical Elasticity written by Leonid P Lebedev and published by World Scientific. This book was released on 2009-09-03 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


An Introduction to the Theory of Elasticity

An Introduction to the Theory of Elasticity

Author: R. J. Atkin

Publisher: Courier Corporation

Published: 2013-02-20

Total Pages: 272

ISBN-13: 0486150992

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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.


Book Synopsis An Introduction to the Theory of Elasticity by : R. J. Atkin

Download or read book An Introduction to the Theory of Elasticity written by R. J. Atkin and published by Courier Corporation. This book was released on 2013-02-20 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 the Mathematical Theory of Vibrations of Elastic Plates

An Introduction to the Mathematical Theory of Vibrations of Elastic Plates

Author: Raymond David Mindlin

Publisher: World Scientific

Published: 2006

Total Pages: 211

ISBN-13: 9812772499

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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. Sample Chapter(s). Chapter 1: Elements of the Linear Theory of Elasticity (416 KB). Contents: Elements of the Linear Theory of Elasticity; Solutions of the Three-Dimensional Equations; Infinite Power Series of Two-Dimensional Equations; Zero-Order Approximation; First-Order Approximation; Intermediate Approximations. Readership: Researchers in mechanics, civil and mechanical engineering and applied mathematics.


Book Synopsis An Introduction to the Mathematical Theory of Vibrations of Elastic Plates by : Raymond David Mindlin

Download or read book An Introduction to the Mathematical Theory of Vibrations of Elastic Plates written by Raymond David Mindlin and published by World Scientific. This book was released on 2006 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Sample Chapter(s). Chapter 1: Elements of the Linear Theory of Elasticity (416 KB). Contents: Elements of the Linear Theory of Elasticity; Solutions of the Three-Dimensional Equations; Infinite Power Series of Two-Dimensional Equations; Zero-Order Approximation; First-Order Approximation; Intermediate Approximations. Readership: Researchers in mechanics, civil and mechanical engineering and applied mathematics.


Three-Dimensional Elasticity

Three-Dimensional Elasticity

Author:

Publisher: Elsevier

Published: 1988-04-01

Total Pages: 495

ISBN-13: 0080875416

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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.


Book Synopsis Three-Dimensional Elasticity by :

Download or read book Three-Dimensional Elasticity written by and published by Elsevier. This book was released on 1988-04-01 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Mathematical Foundations of Elasticity

Mathematical Foundations of Elasticity

Author: Jerrold E. Marsden

Publisher: Courier Corporation

Published: 2012-10-25

Total Pages: 578

ISBN-13: 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.


Book Synopsis Mathematical Foundations of Elasticity by : Jerrold E. Marsden

Download or read book Mathematical Foundations of Elasticity written by Jerrold E. Marsden and published by Courier Corporation. This book was released on 2012-10-25 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


A Treatise on the Mathematical Theory of Elasticity

A Treatise on the Mathematical Theory of Elasticity

Author: Augustus Edward Hough Love

Publisher:

Published: 1927

Total Pages: 674

ISBN-13:

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Book Synopsis A Treatise on the Mathematical Theory of Elasticity by : Augustus Edward Hough Love

Download or read book A Treatise on the Mathematical Theory of Elasticity written by Augustus Edward Hough Love and published by . This book was released on 1927 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt:


Introduction to Mathematical Elasticity

Introduction to Mathematical Elasticity

Author: Michael J. Cloud

Publisher: World Scientific

Published: 2009

Total Pages: 317

ISBN-13: 9814273732

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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.


Book Synopsis Introduction to Mathematical Elasticity by : Michael J. Cloud

Download or read book Introduction to Mathematical Elasticity written by Michael J. Cloud and published by World Scientific. This book was released on 2009 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Differential Geometry with Applications to Elasticity

An Introduction to Differential Geometry with Applications to Elasticity

Author: Philippe G. Ciarlet

Publisher: Springer Science & Business Media

Published: 2006-06-28

Total Pages: 212

ISBN-13: 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].


Book Synopsis An Introduction to Differential Geometry with Applications to Elasticity by : Philippe G. Ciarlet

Download or read book An Introduction to Differential Geometry with Applications to Elasticity written by Philippe G. Ciarlet and published by Springer Science & Business Media. This book was released on 2006-06-28 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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].


Continuum Mechanics and Linear Elasticity

Continuum Mechanics and Linear Elasticity

Author: Ciprian D. Coman

Publisher: Springer Nature

Published: 2019-11-02

Total Pages: 519

ISBN-13: 9402417710

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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).


Book Synopsis Continuum Mechanics and Linear Elasticity by : Ciprian D. Coman

Download or read book Continuum Mechanics and Linear Elasticity written by Ciprian D. Coman and published by Springer Nature. This book was released on 2019-11-02 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).