Thermoelastic Models of Continua

ISBN-13: 9781402023095 / Angielski / Twarda / 2004 / 304 str.

D. Iesan; Dorin Iesan

Opis

This volume is concerned with the basic problems of the theory of thermoelasticity for three models of continuous bodies: materials with voids, micropolar solids and nonsimple bodies.
Beginning with the basic laws of thermodynamics, the theory of thermoelastic materials with voids is treated. Two subsequent chapters cover the analysis of the linear theory of micropolar thermoelastic bodies. The book concludes with a study of nonsimple thermoelastic materials, which are characterised by the inclusion of higher gradients of displacement in the basic postulates. Relevant examples and exercises which illustrate the theory are given throughout the text.
The book should be of interest to mathematicians and specialists working in the fields of elasticity, thermoelasticity, civil engineering and geophysics.

Recenzje

From the reviews:

"The present monograph of lesan is a valuable contribution to the mathematical foundation of the theory of thermoelasticity of continuous bodies. ... his goal is 'to present a unified and systematic treatment of some results established in the theory of generalized models of thermoelastic bodies', and in my opinion he reaches this aim in a very good manner ... . The book can be a helpful tool not only for pure and applied mathematicians but also for physicists as well as for engineers ... ." (M. Fuchs, ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 86 (11), 2006)

"The book is complementary to the well-known monographs on the non-classical theories of thermoelasticity ... . And it is written by one of the experts in the field, who has contributed to the development of the classical dynamic thermoelasticity and its extensions immensely. ... On the whole this is a valuable monograph in the field of solid mechanics that should prove useful to a wide range of researchers for many years to come." (J. Ignaczak, Mathematical Reviews, Issue 2006 e)

Spis treści

Introduction. 1: Thermoelastic Materials with Voids. 1.1. Preliminaries. The Laws of Thermodynamics. 1.2. Constitutive Equations. Thermodynamic Restrictions. 1.3. Boundary-Initial-Value Problems. 1.4. Continuous Data Dependence and Uniqueness Results. 1.5. The Linear Theory. 2: Dynamic Theory. 2.1. Uniqueness Results. 2.2. Reciprocal Theorem. Applications. 2.3. Homogeneous and Isotropic Bodies. 2.4. Acceleration Waves. 2.5. Harmonic Waves. 2.6. Concentrated Loads. 2.7. Radiation Conditions. 2.8. Potentials. 3: Equilibrium Theory. 3.1. Thermoelastic States. 3.2. The Thermoelastic Plane Strain. 3.3. Exercises. 4: Prestressed Thermoelastic Bodies. 4.1. Equations of Perturbed Motion. 4.2. An Existence Result. 5: Thermoelastic Cosserat Continua. 5.1. The Linear Theory of Micropolar Thermoelasticity. 5.2. Thermoelastic Processes. Boundary-Initial-Value Problem. 5.3. Reciprocity. Existence and Uniqueness Results. 5.4. Variational Theorem. 5.5. Homogeneous and Isotropic Solids. Plane Waves. 5.6. A Representation of Galerkin Type. Fundamental Solutions. 5.7. Transient Waves. 5.8. Plane Strain Problem. 5.9. Bending of Micropolar Thermoelastic Plates. 5.10. A Generalized Theory of Micropolar Thermoelasticity. 6: Thermoelastostatics of Micropolar Bodies. 6.1. Boundary Value Problems. Basic Theorems. 6.2. Special Results for Homogeneous and Isotropic Bodies. 6.3. The Equilibrium Plane Problems. 6.4. Exercises. 6.5. Thermal Stresses in Beams. 6.6. Cylinders Composed of Different Materials. 7: Nonsimple Materials. 7.1. The Nonlinear Thermoelasticity. 7.2. Uniqueness and Continuous Dependence results. 7.3. Linear Theories. 7.4. Isotropic Bodies. 7.5. A Grade Consistent Theory of Micropolar Thermoelasticity. References. Index.