Introduction to Mechanics of Continua

by William Prager

• ISBN13: 9780486438092
• ISBN10: 0486438090
• Edition: Reprint
• Format: Hardcover
• Copyright: 2004-08-25
• Publisher: Dover Publications

Summary

A classic in the field, this book meets the demands of courses that establish groundwork in hydrodynamics, gas dynamics, plasticity and elasticity, and it provides typical continua problems for nonspecialists. The author addresses the major aspects of continuum studies: geometrical foundations, state of stress, instantaneous motion, fundamental laws, perfect fluids, viscous fluids, visco-plastic and perfectly plastic materials, hypoelastic materials, finite strain, and elastic and hyperelastic materials. The text's broad converge and numerous applications include more than 160 problems and examples, and the only prerequisites are first- and second-year college calculus. 1961 ed.

Author Biography

William Prager L. Herbert Ballou University Professor Brown University

Table of Contents

Geometrical Foundations
Introduction	p. 3
Transformation of coordinates	p. 4
Scalar and vector	p. 8
Tensor	p. 11
Generalization	p. 14
The [epsilon]-tensor	p. 17
Principal axes of a symmetric tensor of the second order	p. 21
Tensor fields	p. 26
Integral theorems	p. 28
Curvilinear coordinates	p. 34
Problems	p. 38
State of Stress
Stress tensor	p. 43
Conditions of equilibrium	p. 45
Principal stresses and principal shearing stresses	p. 47
Mohr's representation of states of stress; Plane state of stress	p. 50
Cauchy's stress quadrics	p. 55
Hydrostatics	p. 56
Problems	p. 59
Instantaneous Motion
Rate of rotation and rate of deformation	p. 62
Plane instantaneous motion	p. 67
Conditions of integrability	p. 70
Material rates of change	p. 73
Problems	p. 78
Fundamental Laws
Conservation of mass	p. 81
Momentum theorem	p. 83
Moment of momentum theorem	p. 85
Energy theorem	p. 86
Simple constitutive equations	p. 87
Problems	p. 92
Perfect Fluids
Equation of motion and vortex theorems	p. 95
Steady flow	p. 98
Irrotational flow	p. 100
Problems	p. 110
Viscous Fluids
Fundamental equations; Similarity	p. 114
Incompressible fluid: rigorous solutions	p. 118
Incompressible fluid: boundary layer equations	p. 124
Incompressible fluid: non-Newtonian behavior	p. 129
Problems	p. 132
Visco-plastic and Perfectly Plastic Materials
Constitutive equation	p. 136
Equation of motion	p. 138
Boundary layer equations	p. 141
Plane plastic flow	p. 144
Problems	p. 150
Hypoelastic Materials; Classical Theory of Elasticity
Stress rate	p. 154
Hypoelastic materials	p. 156
Hypoelastic materials in the neighborhood of stress-free state	p. 160
Fundamental equations of elastostatics	p. 162
Torsion of cylindrical bars	p. 166
Extremum principles	p. 172
Elastic waves	p. 178
Problems	p. 184
Finite Strain
Almansi's strain tensor	p. 188
Green's strain tensor	p. 193
Other strain tensors	p. 196
Lagrange's and Kirchhoff's stress tensors	p. 199
Elastic and Hyperelastic Materials
Elastic materials	p. 204
Hyperelastic materials	p. 205
Incompressible hyperelastic materials	p. 209
Uniqueness and stability	p. 215
Index	p. 223
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