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Theory Of Elasticity For Scientists And Engineers

Author: Teodor M. Atanackovic
Publisher: Springer Science & Business Media
ISBN: 1461213304
Size: 79.98 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.

Theory Of Elasticity

Author: A.I. Lurie
Publisher: Springer Science & Business Media
ISBN: 9783540264552
Size: 29.20 MB
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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

Author: Aldo Maceri
Publisher: Springer Science & Business Media
ISBN: 9783642113925
Size: 29.81 MB
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This book provides the analytical tools for calculating stresses and deformations in a strained elastic body. It gives engineers, in a simple form, a clear indication of the necessary fundamental knowledge of the theory of elasticity.

The Linearized Theory Of Elasticity

Author: William S. Slaughter
Publisher: Springer Science & Business Media
ISBN: 1461200938
Size: 21.66 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.

Fundamentals Of Engineering Elasticity

Author: Sidney F. Borg
Publisher: World Scientific
ISBN: 9789810201654
Size: 69.28 MB
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The two fundamental premises of the original edition have been adhered to, namely: To obtain a real understanding of ?mechanics of materials? we must go back to the beginnings of the fields i.e the linearized mathematical theory of elasticity; Secondly, the subject of engineering elasticity is a natural one to use in introducing to the undergraduate engineering student the important topic of tensors.

Elasticity And Plasticity

Author: J. N. Goodier
Publisher: Courier Dover Publications
ISBN: 048681047X
Size: 20.83 MB
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This volume comprises two classic essays on the mathematical theories of elasticity and plasticity by authorities in this area of engineering science. Undergraduate and graduate students in engineering as well as professional engineers will find these works excellent texts and references. The Mathematical Theory of Elasticity covers plane stress and plane strain in the isotropic medium, holes and fillets of assignable shapes, approximate conformal mapping, reinforcement of holes, mixed boundary value problems, the third fundamental problem in two dimensions, eigensolutions for plane and axisymmetric states, anisotropic elasticity, thermal stress, elastic waves induced by thermal shock, three-dimensional contact problems, wave propagation, traveling loads and sources of disturbance, diffraction, and pulse propagation. The Mathematical Theory of Plasticity explores the theory of perfectly plastic solids, the theory of strain-hardening plastic solids, piecewise linear plasticity, minimum principles of plasticity, bending of a circular plate, and other problems.

History Of Strength Of Materials

Author: Stephen Timoshenko
Publisher: Courier Corporation
ISBN: 9780486611877
Size: 14.76 MB
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Strength of materials is that branch of engineering concerned with the deformation and disruption of solids when forces other than changes in position or equilibrium are acting upon them. The development of our understanding of the strength of materials has enabled engineers to establish the forces which can safely be imposed on structure or components, or to choose materials appropriate to the necessary dimensions of structures and components which have to withstand given loads without suffering effects deleterious to their proper functioning. This excellent historical survey of the strength of materials with many references to the theories of elasticity and structures is based on an extensive series of lectures delivered by the author at Stanford University, Palo Alto, California. Timoshenko explores the early roots of the discipline from the great monuments and pyramids of ancient Egypt through the temples, roads, and fortifications of ancient Greece and Rome. The author fixes the formal beginning of the modern science of the strength of materials with the publications of Galileo's book, "Two Sciences," and traces the rise and development as well as industrial and commercial applications of the fledgling science from the seventeenth century through the twentieth century. Timoshenko fleshes out the bare bones of mathematical theory with lucid demonstrations of important equations and brief biographies of highly influential mathematicians, including: Euler, Lagrange, Navier, Thomas Young, Saint-Venant, Franz Neumann, Maxwell, Kelvin, Rayleigh, Klein, Prandtl, and many others. These theories, equations, and biographies are further enhanced by clear discussions of the development of engineering and engineering education in Italy, France, Germany, England, and elsewhere. 245 figures.

Elasticity In Engineering Mechanics

Author: Arthur P. Boresi
Publisher: John Wiley & Sons
ISBN: 9780471316145
Size: 12.73 MB
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Comprehensive, accessible, and LOGICAL–an outstanding treatment of elasticity in engineering mechanics Arthur Boresi and Ken Chong′s Elasticity in Engineering Mechanics has been prized by many aspiring and practicing engineers as an easy–to–navigate guide to an area of engineering science that is fundamental to aeronautical, civil, and mechanical engineering, and to other branches of engineering. With its focus not only on elasticity theory but also on concrete applications in real engineering situations, this acclaimed work is a core text in a spectrum of courses at both the undergraduate and graduate levels, and a superior reference for engineering professionals. With more than 200 graphs, charts, and tables, this Second Edition includes: ∗ A complete solutions manual for instructors ∗ Clear explorations of such topics as deformation and stress, stress–strain–temperature relations, plane elasticity with respect to rectangular and polar coordinates, thermal stresses, and end loads ∗ Discussions of deformation and stress treated separately for clarity, with emphasis on both their independence and mathematical similarities ∗ An overview of the mathematical preliminaries to all aspects of elasticity, from stress analysis to vector fields, from the divergence theorem to tensor algebra ∗ Real–world examples and problem sets illustrating the most common elasticity solutions–such as equilibrium equations, the Galerkin vector, and Kelvin′s problem ∗ A series of appendixes covering advanced topics such as complex variables and couple–stress theory


Author: J. R. Barber
Publisher: Springer Science & Business Media
ISBN: 9048138086
Size: 46.95 MB
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The subject of Elasticity can be approached from several points of view, - pending on whether the practitioner is principally interested in the mat- matical structure of the subject or in its use in engineering applications and, in the latter case, whether essentially numerical or analytical methods are envisaged as the solution method. My ?rst introduction to the subject was in response to a need for information about a speci?c problem in Tribology. As a practising Engineer with a background only in elementary Mechanics of - terials, I approached that problem initially using the concepts of concentrated forces and superposition. Today, with a rather more extensive knowledge of analytical techniques in Elasticity, I still ?nd it helpful to go back to these roots in the elementary theory and think through a problem physically as well as mathematically, whenever some new and unexpected feature presents di?culties in research. This way of thinking will be found to permeate this book. My engineering background will also reveal itself in a tendency to work examples through to ?nal expressions for stresses and displacements, rather than leave the derivation at a point where the remaining manipulations would be mathematically routine. The ?rst edition of this book, published in 1992, was based on a one semester graduate course on Linear Elasticity that I have taught at the U- versity of Michigan since 1983.