Continuum mechanics: the birthplace of mathematical models

Medientyp: Buch

Titel: Continuum mechanics : the birthplace of mathematical models

Enthält: Cover; Title Page; Copyright; Dedication; Preface; Contents; Chapter 1 Geometric Setting; 1.1 Vectors and Euclidean Point Space; 1.1.1 Vectors; 1.1.2 Euclidean Point Space; 1.1.3 Summary; 1.2 Tensors; 1.2.1 First-Order Tensors and Vectors; 1.2.2 Second-Order Tensors; 1.2.3 Cross Products, Triple Products, and Determinants; 1.2.4 Orthogonal Tensors; 1.2.5 Invariants of a Tensor; 1.2.6 Derivatives of Tensor-Valued Functions; 1.2.7 Summary; Chapter 2 Kinematics I: The Calculus of Motion; 2.1 Bodies, Motions, and Deformations; 2.1.1 Deformation; 2.1.2 Examples of Motions; 2.1.3 Summary
2.2 Derivatives of Motion2.2.1 Time Derivatives; 2.2.2 Derivatives With Respect to Position; 2.2.3 The Deformation Gradient; 2.2.4 Summary; 2.3 Pathlines, Streamlines, and Streaklines; 2.3.1 Three Types of Arc; 2.3.2 An Example; 2.3.3 Summary; 2.4 Integrals Under Motion; 2.4.1 Arc, Surface, and Volume Integrals; 2.4.2 Reynolds Transport Theorem; 2.4.3 Summary; Chapter 3 Kinematics II: Strain and its Rates; 3.1 Strain; 3.1.1 Symmetric Tensors; 3.1.2 Polar Decomposition and the Deformation Gradient; 3.1.3 Examples; 3.1.4 Cauchy-Green and Strain Tensors; 3.1.5 Strain Invariants; 3.1.6 Summary
3.2 Infinitesimal Strain3.2.1 The Infinitesimal Strain Tensor; 3.2.2 Summary; 3.3 Strain Rates; 3.3.1 Stretching and Spin Tensors; 3.3.2 Skew Tensors, Spin, and Vorticity; 3.3.3 Summary; 3.4 Vorticity and Circulation; 3.4.1 Circulation; 3.4.2 Summary; 3.5 Observer Transformations; 3.5.1 Changes in Frame of Reference; 3.5.2 Summary; Chapter 4 Balance Laws; 4.1 Mass Balance; 4.1.1 Local Forms of Mass Balance; 4.1.2 Summary; 4.2 Momentum Balance; 4.2.1 Analysis of Stress; 4.2.2 Inertial Frames of Reference; 4.2.3 Momentum Balance in Referential Coordinates; 4.2.4 Summary
4.3 Angular Momentum Balance4.3.1 Symmetry of the Stress Tensor; 4.3.2 Summary; 4.4 Energy Balance; 4.4.1 Thermal Energy Balance; 4.4.2 Summary; 4.5 Entropy Inequality; 4.5.1 Motivation; 4.5.2 Clausius-Duhem Inequality; 4.5.3 Summary; 4.6 Jump Conditions; 4.6.1 Singular Surfaces; 4.6.2 Localization; 4.6.3 Summary; Chapter 5 Constitutive Relations: Examples of Mathematical Models; 5.1 Heat Transfer; 5.1.1 Properties of the Heat Equation; 5.1.2 Summary; 5.2 Potential Theory; 5.2.1 Motivation; 5.2.2 Boundary Conditions; 5.2.3 Uniqueness of Solutions to the Poisson Equation
5.2.4 Maximum Principle5.2.5 Mean Value Property; 5.2.6 Summary; 5.3 Fluid Mechanics; 5.3.1 Ideal Fluids; 5.3.2 An Ideal Fluid in a Rotating Frame of Reference; 5.3.3 Acoustics; 5.3.4 Incompressible Newtonian Fluids; 5.3.5 Stokes Flow; 5.3.6 Summary; 5.4 Solid Mechanics; 5.4.1 Static Displacements; 5.4.2 Elastic Waves; 5.4.3 Summary; Chapter 6 Constitutive Theory; 6.1 Conceptual Setting; 6.1.1 The Need to Close the System; 6.1.2 Summary; 6.2 Determinism and Equipresence; 6.2.1 Determinism; 6.2.2 Equipresence; 6.2.3 Summary; 6.3 Objectivity; 6.3.1 Reducing Functional Dependencies
6.3.2 Summary

Beteiligte: Allen, Myron B. [VerfasserIn]

Erschienen: Hoboken, New Jersey: Wiley, [2016]

Umfang: xv, 268 Seiten; Diagramme; 24 cm

Sprache: Englisch

ISBN: 9781118909379

RVK-Notation: UF 2000 : Kontinuumsmechanik allgemein

Schlagwörter: Angewandte Mathematik > Kontinuumsmechanik

Entstehung:

Anmerkungen: Literaturverzeichnis: Seite 265-268

Beschreibung: Presents a self-contained introduction to continuum mechanics that illustrates how many of the important partial differential equations of applied mathematics arise from continuum modeling principles Written as an accessible introduction, Continuum Mechanics: The Birthplace of Mathematical Models provides a comprehensive foundation for mathematical models used in fluid mechanics, solid mechanics, and heat transfer. The book features derivations of commonly used differential equations based on the fundamental continuum mechanical concepts encountered in various fields, such as engineering, physics, and geophysics. The book begins with geometric, algebraic, and analytical foundations before introducing topics in kinematics. The book then addresses balance laws, constitutive relations, and constitutive theory. Finally, the book presents an approach to multiconstituent continua based on mixture theory to illustrate how phenomena, such as diffusion and porous-media flow, obey continuum-mechanical principles. Continuum Mechanics: The Birthplace of Mathematical Models features: -- Direct vector and tensor notation to minimize the reliance on particular coordinate systems when presenting the theory -- Terminology that is aligned with standard courses in vector calculus and linear algebra -- The use of Cartesian coordinates in the examples and problems to provide readers with a familiar setting -- Over 200 exercises and problems with hints and solutions in an appendix -- Introductions to constitutive theory and multiconstituent continua, which are distinctive for books at this level Continuum Mechanics: The Birthplace of Mathematical Models is an ideal textbook for courses on continuum mechanics for upper-undergraduate mathematics majors and graduate students in applied mathematics, mechanical engineering, civil engineering, physics, and geophysics. The book is also an excellent reference for professional mathematicians, physical scientists, and engineers.

Continuum mechanics : the birthplace of mathematical models

Merkliste

Exemplare

Zentralbibliothek

Nur in Feld suchen:

Zuletzt gesuchte Begriffe:

Zentralbibliothek