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A Course In Elasticity

Author : B. M. Fraeijs de Veubeke
ISBN : LCCN:79133180
Genre : Elastic analysis (Engineering)
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A Course In Elasticity

Author : B. M. Fraeijs de Veubeke
ISBN : STANFORD:36105031421055
Genre : Science
File Size : 51. 72 MB
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This book is based on lecture notes of the late Professor de Veubeke. The subject is presented at a level suitable for graduate students in engineering, physics, or mathematics. Some exposure to linear algebra, complex analysis, variational calculus, or basic continuum mechanics would be helpful. The first third of the book contains the fundamentals of the theory of elasticity. Kinematics of continuous media, the notions of stress and equilibrium, conservation of energy, 'and the elastic constitutive law are each treated first in a nonlinear context, then specialized to the linear case. The remainder of the book is given to three classic applications of the theory, each supplemented by original re sults based on the use of complex variables. Each one of the three topics - Saint-Venant's theory of prismatic beams, plane deformations, and the bending of plates - is first pre sented and analyzed in general, then rounded out with numerous specific and sometimes novel examples. The following notational conventions are generally in force, except where noted to the contrary: lower case boldface letters denote vectors or triples of Cartesian co ordinates, upper case boldface letters denote 3 x 3 matrices, repeated lower case Latin subscripts are summed over (1,2,3), and non-repeated lower case Latin subscripts are assumed to range over (1,2,3).

A Course In Elasticity

Author : B. M. Fraeijs de Veubeke
ISBN : 9781461262268
Genre : Science
File Size : 48. 20 MB
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This book is based on lecture notes of the late Professor de Veubeke. The subject is presented at a level suitable for graduate students in engineering, physics, or mathematics. Some exposure to linear algebra, complex analysis, variational calculus, or basic continuum mechanics would be helpful. The first third of the book contains the fundamentals of the theory of elasticity. Kinematics of continuous media, the notions of stress and equilibrium, conservation of energy, 'and the elastic constitutive law are each treated first in a nonlinear context, then specialized to the linear case. The remainder of the book is given to three classic applications of the theory, each supplemented by original re sults based on the use of complex variables. Each one of the three topics - Saint-Venant's theory of prismatic beams, plane deformations, and the bending of plates - is first pre sented and analyzed in general, then rounded out with numerous specific and sometimes novel examples. The following notational conventions are generally in force, except where noted to the contrary: lower case boldface letters denote vectors or triples of Cartesian co ordinates, upper case boldface letters denote 3 x 3 matrices, repeated lower case Latin subscripts are summed over (1,2,3), and non-repeated lower case Latin subscripts are assumed to range over (1,2,3).

Finite Elasticity And Viscoelasticity

Author : Aleksey D. Drozdov
ISBN : 9810224338
Genre : Science
File Size : 54. 26 MB
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This book provides a systematic and self-consistent introduction to the nonlinear continuum mechanics of solids, from the main axioms to comprehensive aspects of the theory. The objective is to expose the most intriguing aspects of elasticity and viscoelasticity with finite strains in such a way as to ensure mathematical correctness, on the one hand, and to demonstrate a wide spectrum of physical phenomena typical only of nonlinear mechanics, on the other.A novel aspect of the book is that it contains a number of examples illustrating surprising behaviour in materials with finite strains, as well as comparisons between theoretical predictions and experimental data for rubber-like polymers and elastomers.The book aims to fill a gap between mathematicians specializing in nonlinear continuum mechanics, and physicists and engineers who apply the methods of solid mechanics to a wide range of problems in civil and mechanical engineering, materials science, and polymer physics. The book has been developed from a graduate course in applied mathematics which the author has given for a number of years.

Finite Elasticity And Viscoelasticity

Author : A D Drozdov
ISBN : 9789814499750
Genre : Mathematics
File Size : 45. 25 MB
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This book provides a systematic and self-consistent introduction to the nonlinear continuum mechanics of solids, from the main axioms to comprehensive aspects of the theory. The objective is to expose the most intriguing aspects of elasticity and viscoelasticity with finite strains in such a way as to ensure mathematical correctness, on the one hand, and to demonstrate a wide spectrum of physical phenomena typical only of nonlinear mechanics, on the other. A novel aspect of the book is that it contains a number of examples illustrating surprising behaviour in materials with finite strains, as well as comparisons between theoretical predictions and experimental data for rubber-like polymers and elastomers. The book aims to fill a gap between mathematicians specializing in nonlinear continuum mechanics, and physicists and engineers who apply the methods of solid mechanics to a wide range of problems in civil and mechanical engineering, materials science, and polymer physics. The book has been developed from a graduate course in applied mathematics which the author has given for a number of years. Contents:Tensor CalculusMechanics of ContinuaConstitutive Equations in Finite ElasticityBoundary Problems in Finite ElasticityVariational Principles in ElasticityConstitutive Models in Finite ViscoelasticityBoundary Problems in Finite Viscoelasticity Readership: Applied mathematicians. keywords:Cauchy Elasticity;Strain Energy Density;Tensor Calculus;Kinematics of Continua;Constitutive Theory;Green Elasticity;Hyperelasticity;Elastic Potentials;Existence;Uniqueness;Boundary Value Problems;Lagrange Principle;Stability;First Order “… a systematic and self-consistent introduction to the nonlinear continuum mechanics of solids, from the main axioms to comprehensive aspects of the theory … fills a gap between mathematicians specializing in nonlinear continuum mechanics, and physicists and engineers who apply the methods of solid mechanics to a wide range of problems in civil and mechanical engineering, materials science, and polymer physics.” Lavoisier-Technique et Documentation “The text should be effective in its intended role as a graduate-level introduction, as well as providing a source of applications and giving a basis for finding some details about the foundations of mechanics. Since there are few, if any, texts having attempted quite the aim of this book … Finite Elasticity and Viscoelasticity can be considered a useful addition to many libraries.” Appl Mech Rev “The textbook includes many exercises of different levels of complexity, which makes the lecture very attractive. The book can be recommended to researchers and students interested in modelling and mathematical problems of nonlinear mechanics of solids.” Mathematical Reviews

Fluid Dynamics And Linear Elasticity

Author : Michael S. Ruderman
ISBN : 9783030192976
Genre : Mathematics
File Size : 53. 15 MB
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​This book provides a concise introduction to continuum mechanics, with a particular emphasis on fluid dynamics, suitable for upper undergraduate students in applied mathematics and related subjects. Starting with a preliminary chapter on tensors, the main topic of the book begins in earnest with the chapters on continuum kinematics and dynamics. Following chapters cover linear elasticity and both incompressible and compressible fluids. Special topics of note include nonlinear acoustics and the theory of motion of viscous thermal conducting compressible fluids. Based on an undergraduate course taught for over a decade, this textbook assumes only familiarity with multivariate calculus and linear algebra. It includes many exercises with solutions and can serve as textbook for lecture courses at the undergraduate and masters level.

The Linearized Theory Of Elasticity

Author : William S. Slaughter
ISBN : 1461266084
Genre : Technology & Engineering
File Size : 72. 57 MB
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This book is derived from notes used in teaching a first-year graduate-level course in elasticity in the Department of Mechanical Engineering at the University of Pittsburgh. This is a modern treatment of the linearized theory of elasticity, which is presented as a specialization of the general theory of continuum mechanics. It includes a comprehensive introduction to tensor analysis, a rigorous development of the governing field equations with an emphasis on recognizing the assumptions and approximations in herent in the linearized theory, specification of boundary conditions, and a survey of solution methods for important classes of problems. Two- and three-dimensional problems, torsion of noncircular cylinders, variational methods, and complex variable methods are covered. This book is intended as the text for a first-year graduate course in me chanical or civil engineering. Sufficient depth is provided such that the text can be used without a prerequisite course in continuum mechanics, and the material is presented in such a way as to prepare students for subsequent courses in nonlinear elasticity, inelasticity, and fracture mechanics. Alter natively, for a course that is preceded by a course in continuum mechanics, there is enough additional content for a full semester of linearized elasticity.

Theory Of Elasticity For Scientists And Engineers

Author : Teodor M. Atanackovic
ISBN : 9781461213307
Genre : Technology & Engineering
File Size : 31. 3 MB
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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 Elastic Structures

Author : Kang Feng
ISBN : 9783662032862
Genre : Science
File Size : 62. 37 MB
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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.

Theory Of Elasticity

Author : L D Landau
ISBN : 075062633X
Genre : Science
File Size : 41. 52 MB
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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 Micropolar Elasticity

Author : Witold Nowacki
ISBN : 9783709127209
Genre : Technology & Engineering
File Size : 42. 53 MB
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Physics Of Elasticity And Crystal Defects

Author : Adrian P. Sutton
ISBN : 9780198860785
Genre : Science
File Size : 61. 89 MB
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Although linear elasticity of defects in solids is well established, this textbook introduces the subject in a novel way by comparing key concepts at the atomic scale and at the usual continuum scale, and it explores the relationships between these treatments. There are exercises to work through, with solutions for instructors from the OUP website.

Elasticity

Author : Martin H. Sadd
ISBN : 9780124104327
Genre : Science
File Size : 46. 87 MB
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Elasticity: Theory, Applications, and Numerics, Third Edition, continues its market-leading tradition of concisely presenting and developing the linear theory of elasticity, moving from solution methodologies, formulations, and strategies into applications of contemporary interest, such as fracture mechanics, anisotropic and composite materials, micromechanics, nonhomogeneous graded materials, and computational methods. Developed for a one- or two-semester graduate elasticity course, this new edition has been revised with new worked examples and exercises, and new or expanded coverage of areas such as spherical anisotropy, stress contours, isochromatics, isoclinics, and stress trajectories. Using MATLAB software, numerical activities in the text are integrated with analytical problem solutions. These numerics aid in particular calculations, graphically present stress and displacement solutions to problems of interest, and conduct simple finite element calculations, enabling comparisons with previously studied analytical solutions. Online ancillary support materials for instructors include a solutions manual, image bank, and a set of PowerPoint lecture slides. Thorough yet concise introduction to linear elasticity theory and applications Only text providing detailed solutions to problems of nonhomogeneous/graded materials New material on stress contours/lines, contact stresses, curvilinear anisotropy applications Further and new integration of MATLAB software Addition of many new exercises Comparison of elasticity solutions with elementary theory, experimental data, and numerical simulations Online solutions manual and downloadable MATLAB code

Course Of Theoretical Physics Vol 7 Theory Of Elasticity 3e

Author : Landau
ISBN : 8181477928
Genre :
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Continuum Mechanics And Linear Elasticity

Author : Ciprian D. Coman
ISBN : 9789402417715
Genre : Technology & Engineering
File Size : 75. 45 MB
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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).

Foundations Of Solid Mechanics

Author : P. Karasudhi
ISBN : 0792307720
Genre : Science
File Size : 28. 9 MB
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This book has been written with two purposes, as a textbook for engineering courses and as a reference book for engineers and scientists. The book is an outcome of several lecture courses. These include lectures given to graduate students at the Asian Institute of Technology for several years, a course on elasticity for University of Tokyo graduate students in the spring of 1979, and courses on elasticity, viscoelasticity and ftnite deformation at the National University of Singapore from May to November 1985. In preparing this book, I kept three objectives in mind: ftrst, to provide sound fundamental knowledge of solid mechanics in the simplest language possible; second, to introduce effective analytical and numerical solution methods; and third, to impress on readers that the subject is beautiful, and is accessible to those with only a standard mathematical background. In order to meet those objectives, the ftrst chapter of the book is a review of mathematical foundations intended for anyone whose background is an elementary knowledge of differential calculus, scalars and vectors, and Newton's laws of motion. Cartesian tensors are introduced carefully. From then on, only Cartesian tensors in the indicial notation, with subscript as indices, are used to derive and represent all theories.

Three Dimensional Elasticity

Author : Philippe G. Ciarlet
ISBN : 044481776X
Genre : Mathematics
File Size : 64. 42 MB
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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.

Elasticity And Plasticity Of Large Deformations

Author : Albrecht Bertram
ISBN : 9783030723286
Genre : Deformations (Mechanics)
File Size : 46. 15 MB
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This book presents an introduction to material theory and, in particular, to elasticity, plasticity and viscoelasticity, to bring the reader close to the frontiers of today's knowledge in these particular fields. It starts right from the beginning without assuming much knowledge of the subject. Hence, the book is generally comprehensible to all engineers, physicists, mathematicians, and others. At the beginning of each new section, a brief Comment on the Literature contains recommendations for further reading. This book includes an updated reference list and over 100 changes throughout the book. It contains the latest knowledge on the subject. Two new chapters have been added in this new edition. Now finite viscoelasticity is included, and an Essay on gradient materials, which have recently drawn much attention.

Three Dimensional Elasticity

Author :
ISBN : 0080875416
Genre : Mathematics
File Size : 78. 20 MB
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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.

A Course In Continuum Mechanics Elastic And Plastic Solids And The Formation Of Cracks

Author : Леонид Иванович Седов
ISBN : STANFORD:36105000599634
Genre : Continuum mechanics
File Size : 61. 44 MB
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