Foundations and Applications of Mechanics, Volume I: Continuum Mechanics explores topics that have come into prominence during the latter half of the twentieth century, such as material frame-indifference, the implications of the second law of thermodynamics, and material symmetry. Jog shows how the classical theories of fluid mechanics, solid mechanics, and rigid-body dynamics follow from the general continuum equations. Written for advanced undergraduate and graduate students, the book provides examples that explore the link between mathematics and physical reality without losing mathematical rigor.
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Zielgruppe
Für höhere Schule und Studium
Maße
Höhe: 229 mm
Breite: 152 mm
Gewicht
ISBN-13
978-0-8493-2414-7 (9780849324147)
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Schweitzer Klassifikation
Autor*in
Indian Institute of Science, Bangalore, India
INTRODUCTION TO TENSORS
Vector Spaces
Vectors in A3
Second-Order Tensors
Higher-Order Tensors
Skew-Symmetric Tensors
Orthogonal Tensors
Symmetric Tensors
Differentiation of Tensors
The Exponential Function
Divergence and Stokes' Theorems
Groups
KINEMATICS
Lagrangian and Eulerian Descriptions
Length, Area, and Volume Elements in the Deformed Configuration
Velocity and Acceleration
Rate of Deformation
Examples of Simple Motions
GOVERNING EQUATIONS
The First Transport Theorem
Conservation of Mass
The Second Transport Theorem
Balance of Linear Momentum
Balance of Angular Momentum
Properties of the Cauchy Stress Tensor
The Equations of Motion in the Reference Configuration
Variational Formulations
Energy Equations
CONSTITUTIVE EQUATIONS
Frame of Reference
Transformation of Kinematical Quantities
Principles of Material Frame-Indifference
Constitutive Relations for Simple Materials
Material Symmetry
Classification of Materials
Constitutional Equations for Elastic Materials
LINEARIZED ELASTICITY
Kinematics
Governing Equations
Variational Formulation in Linearized Elasticity
Uniqueness of Solution
THERMOMECHANICS
Frame-Indifference Applied to the First Law of Thermodynamics
Consequences of the Second Law of Thermodynamics
RIGID-BODY DYNAMICS
Bibliography
Index
