Book contents
- Frontmatter
- Contents
- PREFACE
- PREFACE TO THE FIRST EDITION
- CHAPTER I INTRODUCTION
- CHAPTER II THE GENERIC EQUATIONS OF THREE-DIMENSIONAL CONTINUUM MECHANICS
- CHAPTER III LONGITUDINAL MOTION OF STRAIGHT RODS WITH BISYMMETRIC CROSS SECTIONS (BIRODS)
- CHAPTER IV CYLINDRICAL MOTION OF INFINITE CYCLINDRICAL SHELLS (BEAMSHELLS)
- CHAPTER V TORSIONLESS, AXISYMMETRIC MOTION OF SHELLS OF REVOLUTION (AXISHELLS)
- CHAPTER VI SHELLS SUFFERING ONE-DIMENSIONAL STRAINS (UNISHELLS)
- CHAPTER VII GENERAL NONLINEAR MEMBRANE THEORY (INCLUDING WRINKLING)
- CHAPTER VIII GENERAL SHELLS
- APPENDICES
- INDEX
CHAPTER II - THE GENERIC EQUATIONS OF THREE-DIMENSIONAL CONTINUUM MECHANICS
Published online by Cambridge University Press: 06 January 2010
- Frontmatter
- Contents
- PREFACE
- PREFACE TO THE FIRST EDITION
- CHAPTER I INTRODUCTION
- CHAPTER II THE GENERIC EQUATIONS OF THREE-DIMENSIONAL CONTINUUM MECHANICS
- CHAPTER III LONGITUDINAL MOTION OF STRAIGHT RODS WITH BISYMMETRIC CROSS SECTIONS (BIRODS)
- CHAPTER IV CYLINDRICAL MOTION OF INFINITE CYCLINDRICAL SHELLS (BEAMSHELLS)
- CHAPTER V TORSIONLESS, AXISYMMETRIC MOTION OF SHELLS OF REVOLUTION (AXISHELLS)
- CHAPTER VI SHELLS SUFFERING ONE-DIMENSIONAL STRAINS (UNISHELLS)
- CHAPTER VII GENERAL NONLINEAR MEMBRANE THEORY (INCLUDING WRINKLING)
- CHAPTER VIII GENERAL SHELLS
- APPENDICES
- INDEX
Summary
Each of Chapters III–V and VIII, which are devoted, respectively, to birods, beamshells, axishells, and general shells, begins with a derivation of the equations of motion by a descent from the equations of balance of translational and rotational momentum of a three-dimensional material continuum. These equations are written in integral-impulse form, which allows us to account for discontinuities in internal and external variables. Later, appropriate forms of the Second Law of Thermodynamics are derived by descent from the three-dimensional, integral form of the Clausius-Duhem inequality.
The present chapter summarizes those laws of three-dimensional continuum mechanics relevant to our approach to shell theory. For a detailed discussion of these laws, we refer the reader to books and articles by Truesdell & Toupin (1960), Truesdell & Noll (1965), Chadwick (1976), Truesdell (1977), Spencer (1980), and Gurtin (1981), among others.
The Integral Equations of Motion
A body B is represented by a set of points called particles that move through three-dimensional Euclidean space. This set of points at time t, St, is called the shape (or image) of B at t; S0 ≡ S is called the reference shape and is assumed to be a connected region.
In classical mechanics, a particular particle pk in a set of n may be identified (i.e., indexed) by a positive integer k = 1,2, …, n. In continuum mechanics a particle in B may be identified by its positionx in S relative to a given Cartesian frame Oxyz represented by the standard orthonormal triad of basis vectors {ex, ey, ez}.
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- The Nonlinear Theory of Elastic Shells , pp. 11 - 20Publisher: Cambridge University PressPrint publication year: 1998