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El. knyga: Continuum Mechanics

  • Formatas: PDF+DRM
  • Serija: Advanced Texts in Physics
  • Išleidimo metai: 17-Apr-2013
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Kalba: eng
  • ISBN-13: 9783662050569
Kitos knygos pagal šią temą:
  • Formatas: PDF+DRM
  • Serija: Advanced Texts in Physics
  • Išleidimo metai: 17-Apr-2013
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Kalba: eng
  • ISBN-13: 9783662050569
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This concise textbook develops step by step the fundamental principles of continuum mechanics. Emphasis is on mathematical clarity, and an extended appendix provides the required background knowledge in linear algebra and tensor calculus. After introducing the basic notions about general kinematics, balance equations, material objectivity and constitutive functions, the book turns to the presentation of rational thermodynamics by stressing the role of Lagrange multipliers in deriving constitutive funcitions from the underlying entropy principle. A brief lecture on extended thermodynamics closes the book. Many examples and exercises round off the material presendted in the chapters. The book addresses primarily advanced undergraduate students in theoretical physics, applied mathematics and materials sciences.



This concise reference work presents the fundamental principles of continuum mechanics. Emphasis is on mathematical clarity and an extended appendix provides the required background knowledge in linear algebra and tensor calculus. After having introduced the basic notions on general kinematics, balance equations, material objectivity and constitutive functions the book turns to a presentation of rational thermodynamics. The book finishing with a section on extended thermodynamics. Many examples and exercises round off the material presented in the chapters. The book is aimed at advanced undergraduate students in theoretical physics, applied mathematics and materials sciences.

Recenzijos

From the reviews:



"The strength of the book lies in the presentation of a very general and rational framework for constitutive formulations and the role thermodynamics plays in these formulations. [ ...] Continuum Mechanics is recommended more as a reference book for students and researchers in applied mechanics and structural mechanics [ ...] The text is also recommended as a textbook for students in the fields of theoretical physics and applied mathematics for which a more rational framework of continuum mechanics is required." (Applied Mechanics Review, 56/3, 2003)



"It is probably a pleasure for all scientists working in the field of continuum mechanics to have a new book by hand which gives a compact and modern introduction into continuum mechanics and thermodynamics and which is enhanced with numerous examples and exercises. the book can be recommended to senior undergraduates and graduate students at the master and PhD level as well as to research scientists and teachers." (Technische Mechanik, Vol. 25 (2), 2005)



"This book contains a modern presentation of the basic principles of continuum mechanics together with an introduction to the basic ideas of rational extended thermodynamics. The book is self-contained, since the appendix contains all relevant material and notation of tensor analysis which is needed in the book. the unified treatment of both rational continuum mechanics and extended thermodynamics is a novelty and renders the book a useful didactic tool." (Paolo Cermelli, Mathematical Reviews, 2005 c)



"The book under review has been written and used in conjunction with an introductory course on continuum mechanics . Each chapter has examples and exercises to supplement the basic material. this is a compact well-written textbook on continuum mechanics, with a strong emphasis on thermodynamics." (Cornelius O. Horgan, SIAM Reviews, Vol. 45 (2), 2003)



"This book is intended primarily asa textbook for graduate students and advanced undergraduate students in theoretical physics, applied mathematics, and engineering sciences. The text can also serve as a reference book for students and researchers in the fields of applied and structural mechanics. The strength of the book lies in the presentation of a very general and rational framework for constitutive formulations and the role thermodynamics plays in these formulations. In summary, Continuum Mechanics is recommended ." (E. DeSantiago, Applied Mechanics Reviews, Vol. 56 (3), 2003)

Kinematics
1(30)
Configuration and Deformation
1(3)
Change of Reference Configuration
4(1)
Strain and Rotation
4(4)
Linear Strain Tensors
8(5)
Motion
13(4)
Material and Spatial Descriptions
14(3)
Relative Deformation
17(3)
Rate of Deformation
20(2)
Change of Frame and Objective Tensors
22(9)
Transformation Property of Motion
25(1)
Property of Some Kinematic Quantities
26(5)
Balance Laws
31(32)
General Balance Equation
31(7)
Field Equation and Jump Condition
35(1)
Balance Equations in Material Coordinates
36(2)
Conservation of Mass
38(3)
Laws of Dynamics
41(10)
Forces and Moments
42(1)
Stress Tensor
43(7)
Conservation of Linear and Angular Momenta
50(1)
Conservation of Energy
51(3)
Summary of Basic Equations
54(4)
Basic Equations in Material Coordinates
56(1)
Boundary Conditions of a Material Body
57(1)
Field Equations in Arbitrary Frames
58(5)
Basic Principles of Constitutive Theories
63(34)
Constitutive Relation
63(2)
Principle of Material Objectivity
65(7)
In Referential Description
68(2)
An Example: a Particular Class of Materials
70(2)
Simple Material Bodies
72(3)
Reduced Constitutive Relations
75(2)
Material Symmetry
77(9)
Constitutive Equation for a Simple Solid Body
81(1)
Constitutive Equation for a Simple Fluid
82(2)
Fluid Crystal within Intrinsic Direction
84(2)
Isotropic Materials
86(3)
Constitutive Equation of an Isotropic Material
88(1)
Fading Memory
89(8)
Linear Viscoelasticity
90(2)
Boltzmann--Volterra Theory of Viscoelasticity
92(1)
Linear Viscoelasticity of Rate Type
93(1)
Remark on Objectivity of Linear Elasticity
94(3)
Representation of Constitutive Functions
97(32)
Materials of Grade n
97(1)
Isotropic Functions
98(14)
Isotropic Elastic Materials and Linear Elasticity
107(2)
Reiner-Rivlin Fluids and Navier-Stokes Fluids
109(2)
Elastic Fluids
111(1)
Representation of Isotropic Functions
112(7)
Isotropic Thermoelastic Solids and Viscous Heat-Conducting Fluids
118(1)
Hemitropic Invariants
119(3)
Anisotropic Invariants
122(7)
Transverse Isotropy and Orthotropy
124(2)
On Irreducibility of Invariant Sets
126(3)
Entropy Principle
129(24)
Entropy Inequality
129(2)
Entropy Principle
131(1)
Thermodynamics of Elastic Materials
132(7)
Linear Thermoelasticity
135(4)
Elastic Materials with Internal Constraints
139(5)
Stability of Equilibrium
144(5)
Thermodynamic Stability Criteria
148(1)
Phase Equilibrium
149(4)
Isotropic Elastic Solids
153(30)
Constitutive Equations
153(2)
Boundary Value Problems in Elasticity
155(2)
Homogeneous Stretch
157(3)
Uniaxial Stretch
158(1)
Biaxial Stretch
159(1)
Symmetric Loading of a Square Sheet
160(6)
Stability of a Square Sheet
162(4)
Simple Shear
166(3)
Pure Shear of a Square Block
169(4)
Finite Deformation of Spherical Shells
173(6)
Eversion of a Spherical Shell
175(1)
Inflation of a Spherical Shell
176(3)
Stability of Spherical Shells
179(4)
Stability under Constant Pressures
180(1)
Stability for an Enclosed Spherical Shell
181(2)
Thermodynamics with Lagrange Multipliers
183(16)
Supply-Free Bodies
183(1)
Viscous Heat-Conducting Fluid
184(5)
General Results
186(2)
Navier--Stokes -Fourier Fluids
188(1)
Method of Lagrange Multipliers
189(5)
An Algebraic Problem
190(1)
Local Solvability
191(3)
Relation Between Entropy Flux and Heat Flux
194(5)
Theorem of Parallel Isotropic Vector Functions
194(5)
Rational Extended Thermodynamics
199(34)
Introduction
199(1)
Formal Structure of System of Balance Equations
200(7)
Symmetric Hyperbolic System
201(3)
Galilean Invariance
204(3)
System of Moment Equations
207(6)
Closure Problem
213(4)
Entropy Principle
214(2)
Formal Procedures
216(1)
Thirteen-Moment Theory of Viscous Heat-Conducting Fluid
217(9)
Field Equations
223(2)
Entropy and Entropy Flux
225(1)
Monatomic Ideal Gases
226(2)
Thirteen-Moment Theory
227(1)
Constitutive Equations
228(1)
Stationary Heat Conduction in Ideal Gases
228(5)
Fourier's Law and Heat Conduction
229(1)
Heat Conduction in Thirteen-Moment Theory
229(3)
Remark on Boundary Value Problems
232(1)
A. Elementary Tensor Analysis 233(56)
Linear Algebra
233(29)
Inner Product
234(1)
Dual Bases
235(3)
Tensor Product
238(5)
Transformation Rules for Components
243(2)
Determinant and Trace
245(6)
Exterior Product and Vector Product
251(3)
Second-Order Tensors
254(2)
Some Theorems of Linear Algebra
256(6)
Tensor Calculus
262(27)
Euclidean Point Space
262(1)
Differentiation
263(9)
Coordinate System
272(3)
Covariant Derivatives
275(2)
Other Differential Operators
277(4)
Physical Components
281(1)
Orthogonal Coordinate Systems
282(7)
References 289(4)
Index 293