North-Holland Series in Applied Mathematics and Mechanics, Volume 25: Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity focuses on the theory of three-dimensional problems, including oscillation theory, boundary value problems, and integral equations. The publication first tackles basic concepts and axiomatization and basic singular solutions. Discussions focus on fundamental solutions of thermoelasticity, fundamental solutions of the couple-stress theory, strain energy and Hooke’s law in the couple-stress theory, and basic equations in terms of stress components. The manuscript then examines uniqueness theorems and singular integrals and integral equations. The book ponders on the potential theory and boundary value problems of elastic equilibrium and steady elastic oscillations. Topics include basic theorems of the oscillation theory, existence of solutions of boundary value problems, integral equations of the boundary value problems, and boundary properties of potential-type integrals. The publication also reviews mixed dynamic problems, couple-stress elasticity, and boundary value problems for media bounded by several surfaces. The text is a dependable source of data for mathematicians and readers interested in three-dimensional problems of the mathematical theory of elasticity and thermoelasticity.

Table of Contents


Chapter I Basic Concepts and Axiomatization

§1. Stresses

1. Internal and External Forces

2. Mass and Surface Forces

3. Force- and Couple-Stresses

§2. Components of stress

1. Components of Force- and Couple-Stress Tensors

2. Expression of the Force-Stress Vector in Terms of Components of the Forcestress Tensor

3. Expression of the Couple-Stress Vector in Terms of Components of the Couplestress Tensor

§3. Displacements and Rotations

1. Displacement Vector

2. Rotation Vector

§4. Basic Equations in Terms of Stress Components

1. Equations of Motion in Classical Elasticity

2. Equations of Motion in the Couple-Stress Theory

§5. Hooke’s Law in Classical Elasticity

1. Components of the Strain Tensor

2. Formulation of Hooke’s Law

3. Isotropic Medium

4. Transversally Isotropic Medium

§6. Strain Energy in Classical Elasticity

1. Law of Energy Conservation

2. Specific Energy of Strain

§7. Strain Energy and Hooke’S Law in the Couple-Stress Theory

1. Law of Energy Conservation

2. Specific Energy of Strain

3. Hooke’s Law

4. Isotropic Medium (with the Centre of Symmetry)

§8. Thermoelasticity. Duhamel-Neumann’s Law

1. Deformation Produced by Temperature Variation

2. Law of Energy Conservation

3. Duhamel-Neumann’s Law

4. Isotropic Medium

§9. Heat Conduction Equation

§10. Stationary Elastic Oscillations

1. Classical Theory of Elasticity

2. Cou


© 1979
North Holland
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