A First Course in Continuum Mechanics

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Cambridge University Press, Jan 17, 2008 - Science - 394 pages
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A concise account of various classic theories of fluids and solids, this book is for courses in continuum mechanics for graduate students and advanced undergraduates. Thoroughly class-tested in courses at Stanford University and the University of Warwick, it is suitable for both applied mathematicians and engineers. The only prerequisites are an introductory undergraduate knowledge of basic linear algebra and differential equations. Unlike most existing works at this level, this book covers both isothermal and thermal theories. The theories are derived in a unified manner from the fundamental balance laws of continuum mechanics. Intended both for classroom use and for self-study, each chapter contains a wealth of exercises, with fully worked solutions to odd-numbered questions. A complete solutions manual is available to instructors upon request. Short bibliographies appear at the end of each chapter, pointing to material which underpins or expands upon the material discussed.
 

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Contents

which provides a concise way to express the nine possible
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2
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representations in particular we write
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χx
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v v vijj ei vijj ei
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Fig 21 Graphical illustration of a regular region consisting of
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242 TensorValued Functions
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Bibliographic Notes
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TO 0
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417 a For the given deformation we find
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5
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which is the desired result
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pmXtdetFXt p0X VXeB t 0
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3 From the definitions of jf2fa if2t Tf2fz and rQt
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6
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E D
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3
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+
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34 Equilibrium
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4
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B
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Fig 42 A small region Ω in B is mapped
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3 Many texts employ the notation v xw in
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Fig 48 Two configurations Bt and Bt in the motion
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2 The field defined by JXt detFXt is typically
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Sa 2L 2QLQT QSaQT
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together with the boundary condition
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FVdetCn FhdetCp0C1
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7
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8
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813 FrameIndifference Considerations
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4 A process in a material body is called reversible
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9
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914 FrameIndifference Considerations
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Page 4 - Truesdell, C. and Toupin, RA, The Classical Field Theories, in Handbuch der Physik, Vol.

About the author (2008)

Oscar Gonzalez is an Associate Professor of Mathematics at the University of Texas. His research interests cover computational and applied mathematical problems related to the large-scale deformations of thin rods and ribbons, and more general three-dimensional bodies. He has contributed articles to numerous journals across mathematics, engineering and chemistry. His current research efforts are directed toward understanding the mechanical properties of DNA at various length scales.

Andrew Stuart is Professor of Mathematics at the University of Warwick. His general research interests cover computational stochastic processes and dynamical systems and his current research efforts are directed mainly towards problems at the interface of applied mathematics and statistics. He has contributed articles to numerous journals across mathematics, engineering and physics and is the recipient of six prizes for his work in Applied Mathematics.

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