Three-Dimensional Problems of Elasticity and Thermoelasticity, Volume 25

1st Edition

Editors: V.D. Kupradze
Hardcover ISBN: 9780444851482
eBook ISBN: 9780080984636
Imprint: North Holland
Published Date: 1st January 1979
72.95 + applicable tax
43.99 + applicable tax
54.95 + applicable tax
Compatible Not compatible
VitalSource PC, Mac, iPhone & iPad Amazon Kindle eReader
ePub & PDF Apple & PC desktop. Mobile devices (Apple & Android) Amazon Kindle eReader
Mobi Amazon Kindle eReader Anything else

Institutional Access

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


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.


© North Holland 1979
North Holland
eBook ISBN:
Hardcover ISBN:

About the Editors

V.D. Kupradze Editor