Theory of Elasticity

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Author: L D Landau,L. P. Pitaevskii,A. M. Kosevich,E.M. Lifshitz

Publisher: Elsevier

ISBN: 0080570690

Category: Science

Page: 195

View: 3027

A comprehensive textbook covering not only the ordinary theory of the deformation of solids, but also some topics not usually found in textbooks on the subject, such as thermal conduction and viscosity in solids.

Theory of Elasticity

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Author: A.I. Lurie

Publisher: Springer Science & Business Media

ISBN: 9783540264552

Category: Technology & Engineering

Page: 1050

View: 1455

The classical theory of elasticity maintains a place of honour in the science ofthe behaviour ofsolids. Its basic definitions are general for all branches of this science, whilst the methods forstating and solving these problems serve as examples of its application. The theories of plasticity, creep, viscoelas ticity, and failure of solids do not adequately encompass the significance of the methods of the theory of elasticity for substantiating approaches for the calculation of stresses in structures and machines. These approaches constitute essential contributions in the sciences of material resistance and structural mechanics. The first two chapters form Part I of this book and are devoted to the basic definitions ofcontinuum mechanics; namely stress tensors (Chapter 1) and strain tensors (Chapter 2). The necessity to distinguish between initial and actual states in the nonlinear theory does not allow one to be content with considering a single strain measure. For this reason, it is expedient to introduce more rigorous tensors to describe the stress-strain state. These are considered in Section 1.3 for which the study of Sections 2.3-2.5 should precede. The mastering of the content of these sections can be postponed until the nonlinear theory is studied in Chapters 8 and 9.

Theory of Elasticity for Scientists and Engineers

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Author: Teodor M. Atanackovic,Ardeshir Guran

Publisher: Springer Science & Business Media

ISBN: 1461213304

Category: Technology & Engineering

Page: 374

View: 2099

This book is intended to be an introduction to elasticity theory. It is as sumed that the student, before reading this book, has had courses in me chanics (statics, dynamics) and strength of materials (mechanics of mate rials). It is written at a level for undergraduate and beginning graduate engineering students in mechanical, civil, or aerospace engineering. As a background in mathematics, readers are expected to have had courses in ad vanced calculus, linear algebra, and differential equations. Our experience in teaching elasticity theory to engineering students leads us to believe that the course must be problem-solving oriented. We believe that formulation and solution of the problems is at the heart of elasticity theory. 1 Of course orientation to problem-solving philosophy does not exclude the need to study fundamentals. By fundamentals we mean both mechanical concepts such as stress, deformation and strain, compatibility conditions, constitu tive relations, energy of deformation, and mathematical methods, such as partial differential equations, complex variable and variational methods, and numerical techniques. We are aware of many excellent books on elasticity, some of which are listed in the References. If we are to state what differentiates our book from other similar texts we could, besides the already stated problem-solving ori entation, list the following: study of deformations that are not necessarily small, selection of problems that we treat, and the use of Cartesian tensors only.

Mathematical Theory of Elasticity

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Author: Richard B. Hetnarski,Jozef Ignaczak

Publisher: CRC Press

ISBN: 9780203502488

Category: Mathematics

Page: 800

View: 2193

This book is devoted to the classical theory of linear elasticity in which both the elastostatics and elastodynamics are discussed. The theory is presented in a modern continuum mechanics setting using direct notation as well as cartesian co-ordinates. Each chapter, except for the first one on the history of elasticity, contains examples with full solutions that illustrate the theory introduced. Also, each chapter except for the first one is supplemented by a set of problems with answers and hints. The book provides new general theorems and applications of elasticity that are complementary to the classical results such as: 3D Compatibility Related Variational Principle of Elastostatics, Pure Stress Treatment of Elastodynamics, Tensorial Classification of Elastic Waves and the Stress Energy Partition Formula for the Classical surface-wave in a semi-space. Due to its explanatory style the book could be useful for graduate students and for beginners in the application of elasticity theory to engineering problems. It may also be useful for researchers in the modern theory of continuum mechanics.

An Introduction to the Theory of Elasticity

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Author: R. J. Atkin,N. Fox

Publisher: Courier Corporation

ISBN: 0486150992

Category: Science

Page: 272

View: 444

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.

The Linearized Theory of Elasticity

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Author: William S. Slaughter

Publisher: Springer Science & Business Media

ISBN: 9780817641177

Category: Mathematics

Page: 543

View: 1181

The book is ideal for a broad audience including graduate students, professionals and researchers in the field of solid mechanics. This new text/reference is an excellent resource designed to introduce students in mechanical or civil engineering to linearized theory of elasticity.

The Mathematical Theory of Elasticity, Second Edition

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Author: Richard B. Hetnarski,Jozef Ignaczak

Publisher: CRC Press

ISBN: 143982889X

Category: Science

Page: 837

View: 7920

Through its inclusion of specific applications, The Mathematical Theory of Elasticity, Second Edition continues to provide a bridge between the theory and applications of elasticity. It presents classical as well as more recent results, including those obtained by the authors and their colleagues. Revised and improved, this edition incorporates additional examples and the latest research results. New to the Second Edition Exposition of the application of Laplace transforms, the Dirac delta function, and the Heaviside function Presentation of the Cherkaev, Lurie, and Milton (CLM) stress invariance theorem that is widely used to determine the effective moduli of elastic composites The Cauchy relations in elasticity A body force analogy for the transient thermal stresses A three-part table of Laplace transforms An appendix that explores recent developments in thermoelasticity Although emphasis is placed on the problems of elastodynamics and thermoelastodynamics, the text also covers elastostatics and thermoelastostatics. It discusses the fundamentals of linear elasticity and applications, including kinematics, motion and equilibrium, constitutive relations, formulation of problems, and variational principles. It also explains how to solve various boundary value problems of one, two, and three dimensions. This professional reference includes access to a solutions manual for those wishing to adopt the book for instructional purposes.