Theory of Elasticity. <gl Spri ringer. and Thermal Stresses. Explanations, Problems and Solutions. Jozef Ignaczak. Naotake Noda Yoshinobu Tanigawa
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1 M. Reza Eslami Richard B. Hetnarski Jozef Ignaczak Naobumi Sumi Naotake Noda Yoshinobu Tanigawa Theory of Elasticity and Thermal Stresses Explanations, Problems and Solutions <gl Spri ringer
2 Contents Part I The Mathematical Theory of Elasticity 1 Mathematical Preliminaries Some Formulas in Tensor Algebra Alternative Definitions of a Vector and of a Tensor Using an Orthogonal Tensor Further Definitions Eigenproblem for a Second Order Tensor A Fourth-Order Tensor C Tensor Fields Integral Theorems Irrotational and Solenoidal Fields Time-Dependent Fields Problems and Solutions Related to the Mathematical Preliminaries 13 2 Fundamentals of Linear Elasticity Deformation of an Elastic Body Compatibility Motion and Equilibrium Equations of Motion Constitutive Relations Isotropic Elastic Body The Cauchy Relations Constitutive Relations for a Thermoelastic Body Problems and Solutions Related to the Fundamentals of Linear Elasticity 43 3 Formulation of Problems of Elasticity Boundary Value Problems of Elastostatics Concept of an Elastic State Concept of a Thermoelastic State Formulation of Boundary Value Problems 69 xi
3 xii Contents 3.5 Uniqueness Formulation of Problems of Nonisothermal Elastostatics Initial-Boundary Value Problems of Elastodynamics Concept of an Elastic Process Formulation of Problems of Isothermal Elastodynamics Problems and Solutions Related to the Formulation of Problems of Elasticity 74 4 Variational Formulation of Elastostatics Minimum Principles The Rayleigh-Ritz Method Variational Principles Compatibility-Related Principle Problems and Solutions Related to Variational Formulation of Elastostatics Variational Principles of Elastodynamics The Hamilton-Kirchhoff Principle Problems and Solutions Related to Variational Principles of Elastodynamics Complete Solutions of Elasticity Complete Solutions of Elastostatics Complete Solutions of Elastodynamics Complete Stress Solution of Elastodynamics Problems and Solutions Related to Complete Solutions of Elasticity Formulation of Two-Dimensional Problems Two-Dimensional Problems of Isothermal Elastostatics Two-Dimensional Problems of Nonisothermal Elastostatics Two-Dimensional Problems of Elastodynamics Two-Dimensional Problems of Nonisothermal Elastodynamics Problems and Solutions Related to Formulation of Two-Dimensional Problems Solutions to Particular Three-Dimensional Boundary Value Problems of Elastostatics Torsion of Circular Bars Problems and Solutions Related to Particular Three-Dimensional Boundary Value Problems of Elastostatics Torsion Problems 212
4 Contents xiii 9 Solutions to Particular Two-Dimensional Boundary Value Problems of Elastostatics The Two-Dimensional Version of Boussinesq-Papkovitch-Neuber Solution for a Body Under Plane Strain Conditions Problems and Solutions Related to Particular Two-Dimensional Boundary Value Problems of Elastostatics Solutions to Particular Three-Dimensional Initial-Boundary Value Problems of Elastodynamics A Spherically Symmetric Green's Function of the Dynamic Theory of Thermal Stresses for an Infinite Elastic Body A Spherically Symmetric Green's Function for a Parabolic Heat Conduction Equation in an Infinite Space Problems and Solutions Related to Particular Three-Dimensional Initial-Boundary Value Problems of Elastodynamics Solutions to Particular Two-Dimensional Initial-Boundary Value Problems of Elastodynamics Dynamic Thermal Stresses in an Infinite Elastic Body Under Plane Strain Conditions Subject to a Time-Dependent Temperature Field Dynamic Thermal Stresses in an Infinite Elastic Body Under Generalized Plane Stress Conditions Subject to a Time-Dependent Temperature Field Problems and Solutions Related to Particular Two-Dimensional Initial-Boundary Value Problems of Elastodynamics One-Dimensional Solutions of Elastodynamics One-Dimensional Field Equations of Isothermal Elastodynamics One-Dimensional Field Equations of Nonisothermal Elastodynamics Problems and Solutions Related to One-Dimensional Initial-Boundary Value Problems of Elastodynamics 276 Part II Thermal Stresses 13 Thermal Stresses in Bars Thermal Stresses in Bars 301
5 xiv Contents 13.2 Problems and Solutions Related to Thermal Stresses in Bars Thermal Stresses in Beams Thermal Stresses in Beams Thermal Stresses in Beams Thermal Stresses in Composite Beams Thermal Deflection in Beams Curved Beams Problems and Solutions Related to Thermal Stresses in Beams Heat Conduction Heat Conduction Equation One-Dimensional Heat Conduction Problems Problems and Solutions Related to Heat Conduction Basic Equations of Thermoelasticity Governing Equations of Thermoelasticity Stress and Strain in a Cartesian Coordinate System Navier's Equations, Compatibility Equations and Boundary Conditions General Solution of Navier's Equations Thermal Stresses in a Cylindrical Coordinate System Thermal Stresses in a Spherical Coordinate System Problems and Solutions Related to Basic Equations of Thermoelasticity Plane Thermoelastic Problems Plane Strain and Plane Stress Problems and Solutions Related to Plane Thermoelastic Problems Thermal Stresses in Circular Cylinders One-Dimensional Problems Plane Problems Two-Dimensional Axisymmetric Problems (r, z) Three-Dimensional Problems Problems and Solutions Related to Thermal Stresses in Circular Cylinders 453
6 Contents xv 19 Thermal Stresses in Spherical Bodies One-Dimensional Problems in Spherical Bodies Two-Dimensional Axisymmetric Problems Problems and Solutions Related to Thermal Stresses in Spherical Bodies Thermal Stresses in Plates Basic Equations for a Rectangular Plate Basic Equations for a Circular Plate Problems and Solutions Related to Thermal Stresses in Plates Thermally Induced Instability Instability of Beam-Column Instability of Plate Problems and Solutions Related to Thermally Induced Instability 539 Part III Thermal Stresses Advanced Theory and Applications 22 Heat Conduction Problems in Rectangular Cartesian Coordinates Steady Two-Dimensional Problems: Separation of Variables Fourier Series Double Fourier Series Bessel Functions and Fourier-Bessel Series Nonhomogeneous Differential Equations and Boundary Conditions Problems and Solutions Related to Heat Conduction Lumped Formulation Problems in Cylindrical Coordinates Problems in Spherical Coordinates Steady-State Two- and Three-Dimensional Problems Thermal Stresses in Beams Thermal Stresses in Beams Deflection Equation of Beams Boundary Conditions Problems and Solutions of Beams Thick Cylinders and Spheres Problems and Solutions of Cylinders and Spheres 653
7 xvi Contents 25 Piping Systems Thermal Expansion of Piping Systems Definition of the Elastic Center Piping Systems in Two-Dimensions Piping Systems in Three-Dimensions Problems and Solutions of Piping Systems Coupled Thermoelasticity Governing Equations, Classical Theory Problems and Solutions of Coupled Thermoelasticity 703 Part IV Numerical Methods 27 The Method of Characteristics Basic Equations for Plane Thermoelastic Waves Characteristics and Characteristic Equations Derivation of Difference Equations and Numerical Procedure Finite-Difference Solution for Temperature Problems and Solutions Related to The Method of Characteristics Finite Element of Coupled Thermoelasticity Galerkin Finite Element One-Dimensional Problem Problems and Solutions Related to Coupled Thermoelasticity Boundary Element, Coupled Thermoelasticity Governing Equations Boundary Integral Equation Fundamental Solution Numerical Formulation Problems and Solutions Related to Coupled Thermoelasticity 763 Errata to Three Books 777 Bibliography 781 Index 783
COPYRIGHTED MATERIAL. Index
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