Introduction to Rational Elasticity

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Introduction to Rational Elasticity

Introduction to Rational Elasticity

  • Author: Chao-cheng Wang,C. Truesdell
  • Publisher: Springer Science & Business Media
  • ISBN: 9789001937102
  • Category: Science
  • Page: 556
  • View: 7028
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An Introduction to Differential Geometry with Applications to Elasticity

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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
  • ISBN: 1402042485
  • Category: Mathematics
  • Page: 210
  • View: 4451
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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].

The Rational Mechanics of Flexible Or Elastic Bodies 1638 - 1788

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The Rational Mechanics of Flexible Or Elastic Bodies 1638 - 1788

The Rational Mechanics of Flexible Or Elastic Bodies 1638 - 1788

Introduction to Vol. X and XI

  • Author: Leonhard Euler
  • Publisher: Springer Science & Business Media
  • ISBN: 9783764314415
  • Category: Mathematics
  • Page: 421
  • View: 9479
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1 We search the concepts and methods ) of the theory of deformable sonds from GALILEO to LAGRANGE. Neither of them achieved much in our subject, but their works serve as 2 termini: With GALILEO's Discorsi in 1638 our matter begins ) (for this is the history of mathematical theory), while LAGRANGE's Mechanique Analitique closed the mechanics of 1) There are three major historical works that bear on our subject. The first is A history of the theory of elasticity and of the strength of materials by I. ToDHUNTER, "edited and completed" by K. PEARSON, Vol. I, Cambridge, 1886. Unfortunately it is necessary to give warning that this book fails to meet the standard set by the histories ToDHUNTER lived to finish. Much of what ToDHUNTER left seems to be rather the rough notes for a book than the book itself; the parts due to PEARSON are fortunately distinguished by square brackets. Researches prior to 1800 are disposed of in the first chapter, 79 pages long and almost entirely the work of PEARSON; as frontispiece to a work whose title restricts it to theory he saw fit to supply a possibly original pen drawing entitled "Rupture. Sur faces of Cast-Iron".

Applied Mechanics Reviews

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Applied Mechanics Reviews

Applied Mechanics Reviews

  • Author: N.A
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mechanics, Applied
  • Page: N.A
  • View: 7054
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Elasticity and Plasticity of Large Deformations

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Elasticity and Plasticity of Large Deformations

Elasticity and Plasticity of Large Deformations

An Introduction

  • Author: Albrecht Bertram
  • Publisher: Springer Science & Business Media
  • ISBN: 3540694005
  • Category: Technology & Engineering
  • Page: 340
  • View: 7835
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This careful and detailed introduction to non-linear continuum mechanics and to elasticity and platicity, with a unique mathematical foundation, starts right from the basics. The general theory of mechanical behaviour is particularized for the broad and important classes of elasticity and plasticity. Brings the reader to the forefront of today's knowledge. A list of notations and an index help the reader finding specific topics.

Topics in Finite Elasticity

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Topics in Finite Elasticity

Topics in Finite Elasticity

  • Author: Morton E. Gurtin
  • Publisher: SIAM
  • ISBN: 9781611970340
  • Category: Elasticity
  • Page: 58
  • View: 641
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Finite elasticity is a theory of elastic materials that are capable of undergoing large deformations. This theory is inherently nonlinear and is mathematically quite complex. This monograph presents a derivation of the basic equations of the theory, a discussion of the general boundary-value problems, and a treatment of several interesting and important special topics such as simple shear, uniqueness, the tensile deformations of a cube, and antiplane shear. The monograph is intended for engineers, physicists, and mathematicians.

Non-Linear Elastic Deformations

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Non-Linear Elastic Deformations

Non-Linear Elastic Deformations

  • Author: R. W. Ogden
  • Publisher: Courier Corporation
  • ISBN: 0486318710
  • Category: Technology & Engineering
  • Page: 544
  • View: 8159
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Classic in the field covers application of theory of finite elasticity to solution of boundary-value problems, analysis of mechanical properties of solid materials capable of large elastic deformations. Problems. References.

Treatise on Classical Elasticity

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Treatise on Classical Elasticity

Treatise on Classical Elasticity

Theory and Related Problems

  • Author: Petre P. Teodorescu
  • Publisher: Springer Science & Business Media
  • ISBN: 9400726163
  • Category: Science
  • Page: 802
  • View: 5773
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Deformable solids have a particularly complex character; mathematical modeling is not always simple and often leads to inextricable difficulties of computation. One of the simplest mathematical models and, at the same time, the most used model, is that of the elastic body – especially the linear one. But, notwithstanding its simplicity, even this model of a real body may lead to great difficulties of computation. The practical importance of a work about the theory of elasticity, which is also an introduction to the mechanics of deformable solids, consists of the use of scientific methods of computation in a domain in which simplified methods are still used. This treatise takes into account the consideration made above, with special attention to the theoretical study of the state of strain and stress of a deformable solid. The book draws on the known specialized literature, as well as the original results of the author and his 50+ years experience as Professor of Mechanics and Elasticity at the University of Bucharest. The construction of mathematical models is made by treating geometry and kinematics of deformation, mechanics of stresses and constitutive laws. Elastic, plastic and viscous properties are thus put in evidence and the corresponding theories are developed. Space problems are treated and various particular cases are taken into consideration. New solutions for boundary value problems of finite and infinite domains are given and a general theory of concentrated loads is built. Anisotropic and non-homogeneous bodies are studied as well. Cosserat type bodies are also modeled. The connection with thermal and viscous phenomena will be considered too. Audience: researchers in applied mathematics, mechanical and civil engineering.

An Introduction to Continuum Mechanics - after Truesdell and Noll

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An Introduction to Continuum Mechanics - after Truesdell and Noll

An Introduction to Continuum Mechanics - after Truesdell and Noll

  • Author: D.R Smith
  • Publisher: Springer Science & Business Media
  • ISBN: 9780792324546
  • Category: Technology & Engineering
  • Page: 352
  • View: 2214
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This book provides a brief introduction to rational continuum mechanics in a form suitable for students of engineering, mathematics and science. The presentation is tightly focused on the simplest case of the classical mechanics of nonpolar materials, leaving aside the effects of internal structure, temperature and electromagnetism, and excluding other mathematical models, such as statistical mechanics, relativistic mechanics and quantum mechanics. Within the limitations of the simplest mechanical theory, the author had provided a text that is largely self-contained. Though the book is primarily an introduction to continuum mechanics, the lure and attraction inherent in the subject may also recommend the book as a vehicle by which the student can obtain a broader appreciation of certain important methods and results from classical and modern analysis.

Introduction to Continuum Mechanics for Engineers

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Introduction to Continuum Mechanics for Engineers

Introduction to Continuum Mechanics for Engineers

  • Author: Ray M. Bowen
  • Publisher: Springer
  • ISBN: N.A
  • Category: Science
  • Page: 261
  • View: 9415
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This textbook is intended to introduce engineering graduate students to the essentials of modern continuum mechanics. The objective of an introductory course is to establish certain classical continuum models within a modern framework. Engineering students need a firm understanding of classical models such as linear viscous fluids (Navier-Stokes theory) and infinitesimal elasticity. This understanding should include an appreciation for the status of the classical models as special cases of general nonlinear continuum models. The relationship of the classical models to nonlinear models is essential in light of the increasing reliance, by engineering designers and researchers, on prepackaged computer codes. These codes are based upon models which have a specific and limited range of validity. Given the danger associated with the use of these computer codes in circumstances where the model is not valid, engineers have a need for an in-depth understanding of continuum mechanics and the continuum models which can be formu lated by use of continuum mechanics techniques. Classical continuum models and others involve a utilization of the balance equations of continuum mechanics, the second law of thermo dynamics, and the principles of material frame indifference and material symmetry. In addition, they involve linearizations of various types. In this text, an effort is made to explain carefully how the governing principles, linearizations, and other approximations combine to yield classical con tinuum models. A fundamental understanding of how these models evolve is most helpful when one attempts to study models which account for a wider array of physical phenomena.