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基本説明
Features: Follows the traditional lectures held at the Ecole Polytechnique. Its high mathematical level of teaching together with abstracts, summaries, formulae boxes, numerous exercises with solutions, makes this book one of most complete books in the area.
Full Description
The scale that concerns the practitioner in mechanics is usually qualified as macroscopic. Indeed, applications are rarely much below the human scale, and in order to be relevant models must be constructed on a similar scale, several orders of magnitude greater than the objects that are normally attributed to the physicist's sphere of interest. The mechanicist is therefore aware of the limits of these models, no matter how elegant their mathematical formulation may be, when the time comes far experimental validation. The mechanicist has a deep concern for the microscopic phenomena at the heart of what is being modelled, exposed by the physicist's research, which can today explain a wide range of material behaviour. The aim of this book is to present the general ideas behind continuum mechanics, thermoelasticity and one-dimensional media. Our approach to constructing mechanical models and modelling forces is based upon the principle oi virtual work. There are several advantages to thismethod. To begin with, it clearly emphasises the key role played by geometrical modelling, leading to mechanically consistent presentations in a systematic way. In addition, by requiring rigorous thought and clear formulation of hypotheses, it identifies the inductive steps and emphasises the need for validation, despite its axiomatic appearance. Moreover, once mastered, it will serve as a productive tool in the reader's later research career. This duality is used in the chapter devoted to variational methods for the solution of thermoelastic problems.
Contents
I. Modelling the Continuum.- II. Deformation.- III. Kinematics.- IV. The Virtual Work Approach to the Modelling of Forces.- V. Modelling Forces in Continuum Mechanics.- VI. Local Analysis of Stresses.- VII. Thermoelasticity.- VIII. Thermoelastic Processes and Equilibrium.- IX. Classic Topics in Three-Dimensional Elasticity.- X. Variational Methods in Linearised Thermoelasticity.- XI. Statics of One-Dimensional Media.- XII. Thermoelastic Structural Analysis.- Appendices.- I. Element of Tensor Calculus.- 1 Tensors on a Vector Space.- 1.1 Definition.- 1.2 First Rank Tensors.- 1.3 Second Rank Tensors.- 2 Tensor Product of Tensors.- 2.1 Definition.- 2.2 Examples.- 2.3 Product Tensors.- 3 Tensor Components.- 3.1 Definition.- 3.2 Change of Basis.- 3.3 Mixed Second Rank Tensors.- 3.4 Twice Contravariant or Twice Covariant Second Rank Tensors.- 3.5 Components of a Tensor Product.- 4 Contraction.- 4.1 Definition of the Contraction of a Tensor.- 4.2 Contracted Multiplication.- 4.3 Doubly Contracted Product of Two Tensors.- 4.4 Total Contraction of a Tensor Product.- 4.5 Defining Tensors by Duality.- 4.6 Invariants of a Mixed Second Rank Tensor.- 5 Tensors on a Euclidean Vector Space.- 5.1 Definition of a Euclidean Space.- 5.2 Application: Deformation in a Linear Mapping.- 5.5 First Rank Euclidean Tensors and the Contracted Product.- 5.6 Second Rank Euclidean Tensors of Simple Product Form and their Contracted Products.- 5.7 Second Rank Euclidean Tensors.- 5.10 Principal Axes and Principal Values of a Real Symmetric Second Rank Euclidean Tensor.- 6 Tensor Fields.- 6.1 Definition.- 6.2 Derivative and Gradient of a Tensor Field.- 6.3 Divergence of a Tensor Field.- 6.4 Curvilinear Coordinates.- Summary of Main Formulas.- II. Differential Operators: Basic Formulas.- 1 Orthonormal Cartesian Coordinates.- 1.1 Coordinates.- 1.2 Vector Field.- 1.3 Scalar Function.- 1.4 Second Rank Tensor Field.- 2 General Cartesian Coordinates.- 2.1 Coordinates.- 2.2 Vector Field.- 2.3 Scalar Function.- 2.4 Second Rank Tensor Field.- 3 Cylindrical Coordinates.- 3.1 Parametrisation.- 3.2 Vector Field.- 3.3 Scalar Function.- 3.4 Symmetric Second Rank Tensor Field.- 4 Spherical Coordinates.- 4.1 Parametrisation.- 4.2 Vector Field.- 4.3 Scalar Function.- 4.4 Symmetric Second Rank Tensor Field.- III. Elements of Plane Elasticity.- 1 Plane Problems.- 2 Plane Strain Thermoelastic Equilibrium.- 2.1 Plane Linearised Strain Tensor.- 2.2 Plane Strain Displacement Field.- 2.3 Plane Strain Thermoelastic Equilibrium in a Homogeneous and Isotropic Material.- 2.4 Solution by the Displacement Method.- 2.5 Solution by the Stress Method.- 2.6 Remarks on the Plane Strain Two-Dimensional Problem.- 2.7 Two-Dimensional Beltrami-Michell Equation.- 2.8 Body Forces Deriving from a Potential. Airy Function.- 2.9 Cylindrical Tube Under Pressure.- 3 Plane Stress Thermoelastic Equilibrium.- 3.1 Plane Stress Tensor.- 3.2 Plane Stress Field.- 3.3 Plane Stress Thermoelastic Equilibrium in a Homogeneous and Isotropic Material.- 3.4 Solution.- 3.5 Cylindrical Tube Under Pressure.- Summary of Main Formulas.
