Introduction To Mathematical Elasticity

Author : L. P. Lebedev,Michael J. Cloud
Publisher : World Scientific
Page : 317 pages
File Size : 40,7 Mb
Release : 2009
Category : Technology & Engineering
ISBN : 9789814273725

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Introduction to Mathematical Elasticity by L. P. Lebedev,Michael J. Cloud Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 40,9 Mb
Release : 2024-06-07
Category : Electronic
ISBN : 9789814467797

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Introduction to Mathematical Elasticity by Anonim Pdf

Author : Raymond David Mindlin,Jiashi Yang
Publisher : World Scientific
Page : 211 pages
File Size : 54,9 Mb
Release : 2006
Category : Technology & Engineering
ISBN : 9789812772497

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An Introduction to the Mathematical Theory of Vibrations of Elastic Plates by Raymond David Mindlin,Jiashi Yang Pdf

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.

Author : Philippe G. Ciarlet
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 42,9 Mb
Release : 2006-06-28
Category : Technology & Engineering
ISBN : 9781402042485

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An Introduction to Differential Geometry with Applications to Elasticity by Philippe G. Ciarlet Pdf

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].

Author : Philippe G. Ciarlet
Publisher : Unknown
Page : 0 pages
File Size : 54,9 Mb
Release : 2021
Category : Elastic plates and shells
ISBN : 1611976790

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Mathematical Elasticity, Volume II by Philippe G. Ciarlet Pdf

The Mathematical Elasticity set contains three self-contained volumes that together provide the only modern treatise on elasticity. They introduce contemporary research on three-dimensional elasticity, the theory of plates, and the theory of shells. Each volume contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study. An extended preface and extensive bibliography have been added to each volume to highlight the progress that has been made since the original publication. The first book, Three-Dimensional Elasticity, covers the modeling and mathematical analysis of nonlinear three-dimensional elasticity. In volume two, Theory of Plates, asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear plate and shallow shell theories. The objective of Theory of Shells, the final volume, is to show how asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear shell theories: membrane, generalized membrane, and flexural. These classic textbooks are for advanced undergraduates, first-year graduate students, and researchers in pure or applied mathematics or continuum mechanics. They are appropriate for courses in mathematical elasticity, theory of plates and shells, continuum mechanics, computational mechanics, and applied mathematics in general.

Author : Anonim
Publisher : Elsevier
Page : 448 pages
File Size : 40,5 Mb
Release : 1988-04-01
Category : Mathematics
ISBN : 0080875416

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Three-Dimensional Elasticity by Anonim Pdf

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.

Author : Augustus Edward Hough Love
Publisher : Courier Corporation
Page : 674 pages
File Size : 53,8 Mb
Release : 1944-01-01
Category : Technology & Engineering
ISBN : 9780486601748

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A Treatise on the Mathematical Theory of Elasticity by Augustus Edward Hough Love Pdf

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.

Author : Philippe G. Ciarlet
Publisher : Unknown
Page : 128 pages
File Size : 48,7 Mb
Release : 1988
Category : Elasticity
ISBN : OCLC:921203199

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Mathematical Elasticity by Philippe G. Ciarlet Pdf

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.

Author : J. Necas,I. Hlavácek
Publisher : Elsevier
Page : 343 pages
File Size : 53,8 Mb
Release : 2017-02-01
Category : Science
ISBN : 9781483291918

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Mathematical Theory of Elastic and Elasto-Plastic Bodies by J. Necas,I. Hlavácek Pdf

The book acquaints the reader with the basic concepts and relations of elasticity and plasticity, and also with the contemporary state of the theory, covering such aspects as the nonlinear models of elasto-plastic bodies and of large deflections of plates, unilateral boundary value problems, variational principles, the finite element method, and so on.

Author : Jerrold E. Marsden,Thomas J. R. Hughes
Publisher : Courier Corporation
Page : 578 pages
File Size : 55,9 Mb
Release : 2012-10-25
Category : Technology & Engineering
ISBN : 9780486142272

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Mathematical Foundations of Elasticity by Jerrold E. Marsden,Thomas J. R. Hughes Pdf

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.

Author : R. J. Atkin,N. Fox
Publisher : Courier Corporation
Page : 272 pages
File Size : 44,5 Mb
Release : 2013-02-20
Category : Science
ISBN : 9780486150994

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An Introduction to the Theory of Elasticity by R. J. Atkin,N. Fox Pdf

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.

Author : Raymond David Mindlin,Jiashi Yang
Publisher : World Scientific
Page : 211 pages
File Size : 40,7 Mb
Release : 2006
Category : Technology & Engineering
ISBN : 9789812703811

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An Introduction to the Mathematical Theory of Vibrations of Elastic Plates by Raymond David Mindlin,Jiashi Yang Pdf

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.

Author : N.I. Muskhelishvili
Publisher : Springer Science & Business Media
Page : 746 pages
File Size : 49,6 Mb
Release : 2013-11-11
Category : Technology & Engineering
ISBN : 9789401730341

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Some Basic Problems of the Mathematical Theory of Elasticity by N.I. Muskhelishvili Pdf

TO THE FIRST ENGLISH EDITION. In preparing this translation, I have taken the liberty of including footnotes in the main text or inserting them in small type at the appropriate places. I have also corrected minor misprints without special mention .. The Chapters and Sections of the original text have been called Parts and Chapters respectively, where the latter have been numbered consecutively. The subject index was not contained in the Russian original and the authors' index represents an extension of the original list of references. In this way the reader should be able to find quickly the pages on which anyone reference is discussed. The transliteration problem has been overcome by printing the names of Russian authors and journals also in Russian type. While preparing this translation in the first place for my own informa tion, the knowledge that it would also become accessible to a large circle of readers has made the effort doubly worthwhile. I feel sure that the reader will share with me in my admiration for the simplicity and lucidity of presentation.

Author : Phillip L. Gould
Publisher : Springer
Page : 256 pages
File Size : 48,6 Mb
Release : 1993-12-09
Category : Technology & Engineering
ISBN : 9780387941004

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Introduction to Linear Elasticity by Phillip L. Gould Pdf

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.

Author : N.I. Muskhelishvili
Publisher : Springer Science & Business Media
Page : 774 pages
File Size : 52,6 Mb
Release : 1977-04-30
Category : Technology & Engineering
ISBN : 9001607012

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Some Basic Problems of the Mathematical Theory of Elasticity by N.I. Muskhelishvili Pdf

TO THE FIRST ENGLISH EDITION. In preparing this translation, I have taken the liberty of including footnotes in the main text or inserting them in small type at the appropriate places. I have also corrected minor misprints without special mention .. The Chapters and Sections of the original text have been called Parts and Chapters respectively, where the latter have been numbered consecutively. The subject index was not contained in the Russian original and the authors' index represents an extension of the original list of references. In this way the reader should be able to find quickly the pages on which anyone reference is discussed. The transliteration problem has been overcome by printing the names of Russian authors and journals also in Russian type. While preparing this translation in the first place for my own informa tion, the knowledge that it would also become accessible to a large circle of readers has made the effort doubly worthwhile. I feel sure that the reader will share with me in my admiration for the simplicity and lucidity of presentation.