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El. knyga: Continuum Mechanics for Engineers

4.29/5 (42 ratings by Goodreads)
(Lafayette College, Easton, Pennsylvania, USA), (University of North Carolina, Charlotte, USA), (California Polytechnic State University, San Luis Obispo, USA)
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A bestselling textbook in its first three editions, Continuum Mechanics for Engineers, Fourth Edition provides engineering students with a complete, concise, and accessible introduction to advanced engineering mechanics. It provides information that is useful in emerging engineering areas, such as micro-mechanics and biomechanics. Through a mastery of this volumes contents and additional rigorous finite element training, readers will develop the mechanics foundation necessary to skillfully use modern, advanced design tools.

Features:











Provides a basic, understandable approach to the concepts, mathematics, and engineering applications of continuum mechanics





Updated throughout, and adds a new chapter on plasticity





Features an expanded coverage of fluids





Includes numerous all new end-of-chapter problems

With an abundance of worked examples and chapter problems, it carefully explains necessary mathematics and presents numerous illustrations, giving students and practicing professionals an excellent self-study guide to enhance their skills.
Preface to the Fourth Edition ix
Authors xi
Nomenclature xiii
1 Continuum Theory
1(1)
1.1
Chapter Learning Outcomes
1(1)
1.2 Continuum Mechanics
1(1)
1.3 Starting Over
2(1)
1.4 Notation
3(2)
2 Essential Mathematics
5(1)
2.1
Chapter Learning Outcomes
5(1)
2.2 Scalars, Vectors and Cartesian Tensors
6(2)
2.3 Tensor Algebra in Symbolic Notation - Summation Convention
8(9)
2.3.1 Kronecker Delta
10(1)
2.3.2 Permutation Symbol
11(1)
2.3.3 ε - δ Identity
11(1)
2.3.4 Tensor/Vector Algebra
12(5)
2.4 Indicial Notation
17(3)
2.5 Matrices and Determinants
20(6)
2.6 Transformations of Cartesian Tensors
26(5)
2.7 Principal Values and Principal Directions of Symmetric Second-Order Tensors
31(7)
2.8 Tensor Fields, Tensor Calculus
38(5)
2.9 Integral Theorems of Gauss and Stokes
43(14)
Problems
46(11)
3 Stress Principles
57(1)
3.1
Chapter Learning Outcomes
57(1)
3.2 Body and Surface Forces, Mass Density
58(1)
3.3 Cauchy Stress Principle
59(2)
3.4 The Stress Tensor
61(5)
3.5 Force and Moment Equilibrium; Stress Tensor Symmetry
66(2)
3.6 Stress Transformation Laws
68(3)
3.7 Principal Stresses; Principal Stress Directions
71(6)
3.8 Maximum and Minimum Stress Values
77(2)
3.9 Mohr's Circles For Stress
79(4)
3.10 Plane Stress
83(4)
3.11 Deviator and Spherical Stress States
87(2)
3.12 Octahedral Shear Stress
89(4)
Problems
93(14)
4 Kinematics of Deformation and Motion
107(1)
4.1
Chapter Learning Outcomes
107(1)
4.2 Particles, Configurations, Deformations and Motion
107(2)
4.3 Material and Spatial Coordinates
109(5)
4.4 Langrangian and Eulerian Descriptions
114(2)
4.5 The Displacement Field
116(1)
4.6 The Material Derivative
117(5)
4.7 Deformation Gradients, Finite Strain Tensors
122(6)
4.8 Infinitesimal Deformation Theory
128(7)
4.9 Compatibility Equations
135(3)
4.10 Stretch Ratios
138(4)
4.11 Rotation Tensor, Stretch Tensors
142(4)
4.12 Velocity Gradient, Rate of Deformation, Vorticity
146(5)
4.13 Material Derivative of Line Elements, Areas, Volumes
151(1)
Problems
156(21)
5 Fundamental Laws and Equations
177(1)
5.1
Chapter Learning Outcomes
177(1)
5.2 Material Derivatives of Line, Surface, and Volume Integrals
178(1)
5.3 Conservation of Mass, Continuity Equation
179(3)
5.4 Linear Momentum Principle, Equations of Motion
182(1)
5.5 Piola-Kirchhoff Stress Tensors, Lagrangian Equations of Motion
183(4)
5.6 Moment of Momentum (Angular Momentum) Principle
187(1)
5.7 Law of Conservation of Energy, The Energy Equation
188(2)
5.8 Entropy and the Clausius-Duhem Equation
190(3)
5.9 The General Balance Law
193(4)
5.10 Restrictions on Elastic Materials by the Second Law of Thermodynamics
197(3)
5.11 Invariance
200(8)
5.12 Restrictions on Constitutive Equations from Invariance
208(2)
5.13 Constitutive Equations
210(1)
References
213(1)
Problems
214(9)
6 Linear Elasticity
223(1)
6.1
Chapter Learning Outcomes
223(1)
6.2 Elasticity, Hooke's Law, Strain Energy
223(4)
6.3 Hooke's Law for Isotropic Media, Elastic Constants
227(4)
6.4 Elastic Symmetry; Hooke's Law for Anisotropic Media
231(5)
6.5 Isotropic Elastostatics and Elastodynamics, Superposition Principle
236(3)
6.6 Saint-Venant Problem
239(12)
6.6.1 Extension
240(1)
6.6.2 Torsion
241(6)
6.6.3 Pure Bending
247(2)
6.6.4 Flexure
249(2)
6.7 Plane Elasticity
251(4)
6.8 Airy Stress Function
255(10)
6.9 Linear Thermoelasticity
265(1)
6.10 Three-Dimensional Elasticity
266(7)
Problems
273(12)
7 Classical Fluids
285(1)
7.1
Chapter Learning Outcomes
285(1)
7.2 Viscous Stress Tensor, Stokesian, and Newtonian Fluids
285(2)
7.3 Basic Equations of Viscous Flow, Navier-Stokes Equations
287(2)
7.4 Specialized Fluids
289(1)
7.5 Steady Flow, Irrotational Flow, Potential Flow
290(5)
7.6 The Bernoulli Equation, Kelvin's Theorem
295(2)
Problems
297(4)
8 Nonlinear Elasticity
301(1)
8.1
Chapter Learning Outcomes
301(1)
8.2 Nonlinear Elastic Behavior
301(3)
8.3 Molecular Approach to Rubber Elasticity
304(5)
8.4 A Strain Energy Theory for Nonlinear Elasticity -
309(4)
8.5 Specific Forms of the Strain Energy
313(1)
8.6 Exact Solution for an Incompressible, Neo-Hookean Material
314(5)
References
319(2)
Problems
321(4)
9 Linear Viscoelasticity
325(1)
9.1
Chapter Learning Outcomes
325(1)
9.2 Viscoelastic Constitutive Equations in Linear Differential Operator Form
326(2)
9.3 One-Dimensional Theory, Mechanical Models
328(4)
9.4 Creep and Relaxation
332(3)
9.5 Superposition Principle, Hereditary Integrals
335(2)
9.6 Harmonic Loadings, Complex Modulus, and Complex Compliance
337(4)
9.7 Three-Dimensional Problems, The Correspondence Principle
341(20)
References
347(1)
Problems
348(13)
10 Plasticity
361(1)
10.1
Chapter Learning Outcomes
361(1)
10.2 One-Dimensional Deformation
362(4)
10.3 Modeling Plasticity
366(3)
10.4 Yield Criteria
369(7)
10.4.1 Tresca-Coulomb Yield Criterion
372(2)
10.4.2 Von Mises Yield Criterion
374(2)
10.4.3 Kinematic Hardening Yield Criterion
376(1)
10.5 Plastic Flow
376(4)
10.5.1 Tresca-Coulomb Yield Criterion
379(1)
10.5.2 Von Mises Yield Criterion
379(1)
10.5.3 Kinematic Hardening Yield Criterion
380(1)
10.6 Plastic Modulus
380(6)
10.6.1 Isotropic Hardening
381(2)
10.6.2 Kinematic Hardening
383(3)
10.7 Elasto-Plastic Constitutive Equations
386(4)
10.7.1 Prandtl-Reuss (J2) Elasto-Plastic Equations
388(1)
10.7.2 Levy-Mises Flow Equations
388(2)
10.7.3 Perfectly Plastic Constitutive Behavior
390(1)
10.8 Deformation Theory of Plasticity
390(1)
10.9 Examples
391(12)
10.9.1 Torsion of a Shaft
391(2)
10.9.2 Bending of a Beam by a Moment
393(3)
10.9.3 Thin-Walled Tube Tension and Torsion
396(2)
References
398(1)
Problems
399(4)
Appendix A General Tensors
403(20)
A.1 Representation of Vectors in General Bases
403(2)
A.2 The Dot Product and the Reciprocal Basis
405(2)
A.3 Components of a Tensor
407(1)
A.4 Determination of the Base Vectors
408(2)
A.5 Derivatives of Vectors
410(4)
A.5.1 Time Derivative of a Vector
410(1)
A.5.2 Covariant Derivative of a Vector
411(3)
A.6 Christoffel Symbols
414(2)
A.6.1 Types of Christoffel Symbols
414(1)
A.6.2 Calculation of the Christoffel Symbols
415(1)
A.7 Covariant Derivatives of Tensors
416(1)
A.8 General Tensor Equations
416(2)
A.9 General Tensors and Physical Components
418(5)
References
421(2)
Appendix B Viscoelastic Creep and Relaxation
423(4)
Index 427
G. Thomas Mase, Ph.D. is Professor of Mechanical Engineering at California Polytechnic State University, San Luis Obispo, California.Dr. Mase is a member of numerous professional societies including the American Society of Mechanical Engineers, American Society for Engineering Education, International Sports Engineering Association, Society of Experimental Mechanics, Pi Tau Sigma, and Sigma Xi.

Ronald E. Smelser, Ph.D., P.E. is Professor and Senior Associate Dean for Academic Affairs in the William States Lee College of Engineering at the University of North Carolina at Charlotte and has his Ph.D. in mechanical engineering from Carnegie Mellon University in 1978.

Jenn Stroud Rossmann, Ph.D. is Professor of Mechanical Engineering at Lafayette College. She earned her PhD in applied physics from the University of California, Berkeley.
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