Thermal Stresses -- Advanced Theory and Applications

This book is intended as an advanced modern textbook and reference handbook on the topic of thermal stresses. It should serve a wide range of readers, in particular, graduate and postgraduate students, scientists, researchers in various industrial and government institutes, and engineers working in mechanical, civil, and aerospace engineering.

This volume covers diverse areas of applied mathematics, continuum mechanics, stress analysis, and mechanical design. This work treats a number of topics not presented in other books on thermal stresses, for example: theory of coupled and generalized thermoelasticity, finite and boundary element method in generalized thermoelasticity, thermal stresses in functionally graded structures, and thermal expansions of piping systems.

As the field of thermal stresses lies at the crossroads of stress analysis, theory of elasticity, heat conduction, and advanced methods of applied mathematics, all these subjects are dealt with in the book to the extent they are necessary. Thus, the book is self-contained, so that the reader should not need to consult other sources while studying the topic. The book starts from basic concepts and principles, and these are developed to more advanced levels as the text progresses. Nevertheless, some basic knowledge on the part of the reader is expected in classical mechanics, stress analysis, and mathematics, including vector and cartesian tensor analysis.

Klappentext

The authors are pleased to present Thermal Stresses - Advanced Theory and Applications. This book will serve a wide range of readers, in particular, gr- uate students, PhD candidates, professors, scientists, researchers in various industrial and government institutes, and engineers. Thus, the book should be considered not only as a graduate textbook, but also as a reference handbook to those working or interested in areas of Applied Mathematics, Continuum Mechanics, Stress Analysis, and Mechanical Design. In addition, the book p- vides extensive coverage of great many theoretical problems and numerous references to the literature. The ?eld of Thermal Stresses lies at the crossroads of Stress Analysis, T- ory of Elasticity, Thermodynamics, Heat Conduction Theory, and advanced methods of Applied Mathematics. Each of these areas is covered to the extend it is necessary. Therefore, the book is self-contained, so that the reader should not need to consult other sources while studying the topic. The book starts from basic concepts and principles, and these are developed to more advanced levels as the text progresses. Nevertheless, some basic preparation on the part of the reader in Classical Mechanics, Stress Analysis, and Mathematics, - cluding Vector and Cartesian Tensor Analysis is expected. While selecting material for the book, the authors made every e?ort to present both classical topics and methods, and modern, or more recent, dev- opments in the ?eld. The book comprises ten chapters.

Inhalt

1 Basic Laws of Thermoelasticity; 1 Introduction; 2 Stresses and Tractions; 3 Equations of Motion ; 4 Coordinate Transformation. Principal Axes; 5 Principal Stresses and Stress Invariants; 6 Displacement and Strain Tensor; 7 Compatibility Equations. Simply Connected Region; 8 Compatibility Conditions. Multiply Connected Regions; 9 Constitutive Laws of Linear Thermoelasticity; 10 Displacement Formulation of Thermoelasticity; 11 Stress Formulation of Thermoelasticity; 12 Two-Dimensional Thermoelasticity; 13 Michell conditions; 2 Thermodynamics of Elastic Continuum; 1 Introduction; 2 Thermodynamics Definitions; 3 First Law of Thermodynamics ; 4 Second Law of Thermodynamics; 5 Variational Formulation of Thermodynamics; 6 Thermodynamics of Elastic Continuum; 7 General Theory of Thermoelasticity ; 8 Free Energy Function of Hookean Materials; 9 Fourier's Law and Heat Conduction Equation ; 10 Generalized Thermoelasticity. Second Sound; 11 Thermoelasticity without Energy Dissipation; 12 Uniqueness Theorem; 13 Variational Principle of Thermoelasticity ; 14 Reciprocity Theorem; 15 Initial and Boundary Conditions; 3 Basic Problems of Thermoelasticity; 1 Introduction; 2 Temperature Distribution for Zero Thermal Stress; 3 Analogy of Thermal Gradient with Body Forces ; 4 General Solution of Thermoelastic Problems; 5 General Solution in Cylindrical Coordinates; 6 Solution of Two-Dimensional Navier Equations;7 Solution of Problems in Spherical Coordinates; 4 Heat Conduction Problems; 1 Introduction; 2 Problems in Rectangular Cartesian Coordinates; 2.1 Steady State One-Dimensional Problems; 2.2 Steady Two-Dimensional Problems. Separation of Variables; 2.3 Fourier Series; 2.4 Double Fourier Series; 2.5 Bessel Functions and Fourier-Bessel series; 2.6 Nonhomogeneous Differential Equations and Boundary Condition; 2.7 Lumped Formulation; 2.8 Steady State Three-Dimensional Problems; 2.9.Transient Problems; 3 Problems in Cylindrical coordinates; 3.1 Steady-State One-Dimensional Problems (Radial Flow); 3.2. Steady -State Two-Dimensional Problems 3.3 Steady-State Three-Dimensional Problems; 3.4 Transient Problems; 4 Problems in Spherical Coordinates; 4.1 Steady-State One-Dimensional Problems; 4.2 Steady-State Two- and Three-Dimensional Problems; 4.3 Transient Problems; 5 Thermal Stresses in Beams; 1 Introduction; 2 Elementary Theory of Thermal Stresses in Beams; 3 Deflection Equation of Beams; 4 Boundary Conditions; 5 Shear Stress in a Beam; 6 Beams of Rectangular Cross Section; 7 Transient Thermal Stresses in Rectangular Beams; 8 . Beam with Internal Heat Generation; 9 Bimetallic Beam; 10 Functionally Graded Beams; 11 Transient Thermal Stresses in Functionally Graded Beams; 12 Thermal Stresses in Thin Curved Beams and Rings; 13 Deflection of Thin Curved Beams and Rings; 6 Disks, Cylinders, and Spheres; 1 Introduction; 2 . Cylinders with Radial Temperature Variation; 3 Thermal Stresses in Disks; 4 Thick Spheres ; 5 Thermal Stresses in a Rotating Disk; 6 Non-Axisymmetrically Heated cylinders; 7 Method of Complex Variables; 8 Functionally Graded Thick Cylinders; 9 Axisymmetric Thermal Stresses in FGM Cylinders; 10.Transient Thermal Stresses in Thick Spheres; 11 Functionality Graded Spheres; 7 Thermal Expansion in Piping Systems; 1 Introduction ; 2 Definition of the Elastic Center; 3 . Piping Systems in Two Dimensions ; 4 Piping Systems in Three-dimensions; 5 Pipelines with Large Radius Elbows; 8 Coupled and Generalized Thermoelasticity; 1 Introduction; 2 Governing Equations of Coupled Thermoelasticity; 3 Coupled Thermoelasticity for Infinite Space; 4 Variable Heat Source; 5 One-Dimensional Coupled Problem; 6 Propagation of Discontinuities; 7 Half-Space Subjected to a Harmonic Temperature; 8 Coupled Thermoelasticity of Thick Cylinders; 9 Green-Naghdi Model of a Layer; 10 Generalized Thermoelasticity of Layers; 11 Generalized Thermoelasticity of Spheres and Cylinders;