Thermal Stress Analyses

PrefaceAcknowledgmentsPrincipal NotationChapter 1. Fundamentals of Thermal Stress Analysis 1.1 Preliminary Remarks on Thermal Stress 1.2 Definition of Strain Components 1.3 Equations of State 1.4 Equations of Equilibrium 1.5 Boundary Conditions 1.5.1 Traction Boundary Conditions 1.5.2 Displacement Boundary Conditions 1.5.3 Mixed Boundary Conditions 1.6 Thermodynamic Considerations and Thermoelastic Coupling 1.7 Minimal Principles in Thermoelasticity 1.8 Solution of the Three-Dimensional Thermoelastic Equations 1.8.1 Various Formulations 1.8.2 Zero Displacements in a Three-Dimensional Body; and a Corollary 1.8.3 Zero Stresses in a Three-Dimensional Body 1.8.4 Summary of Methods of SolutionChapter 2. Two-Dimensional Formulations and Solutions 2.1 Plane Strain Analyses 2.2 Plane Stress Analyses 2.3 Summary of the Thermal Stress Equations in Two Dimensions 2.4 Use of the Airy Stress Function for Solid Structures 2.5 One-Dimensional Thermal Stresses in a Thin Rectangular Slab 2.6 Thick Plate with Temperature Variation through the Thickness Only 2.7 Thermal Stresses in Thin PlatesChapter 3. Membrane Thermal Stresses in Thin Plates 3.1 Thermal Stresses near Hot Spots Infinite Plates 3.2 A Circular Disc with a General Radial Temperature Distribution 3.3 A Solid Circular Disc with an Asymmetrical Temperature Distribution 3.4 A Circular Ring with an Asymmetrical Temperature Distribution 3.5 Thermal Stresses in Finite Rectangular Plates (Method 1) 3.6 Thermal Stresses in Finite Rectangular Plates (Methods 2-4)Chapter 4. Bending Thermal Stresses in Thin Plates 4.1 Theory for Thin Isotropic Plates with Small Deflections 4.2 Theory for Thin Isotropic Plates with Large Deflections 4.3 Boundary Conditions 4.4 Temperature Distributions, T = T(z) 4.4.1 Free Plate of Arbitrary Planform; T = T(z) 4.4.2 Circular Plates; T(z) = -ΔT(z/d) 4.4.3 Rectangular Plates; T(z) = -ΔT(z/d) 4.4.4 Polygonal Plates; T(z) = -ΔT(z/d) 4.4.5 Sundry Solutions; T = T(z) 4.5 Temperature Distribution T=-zΔT(xy)/d 4.5.1 Axisymmetric Bending of Hollow Circular Plates 4.5.2 Bending of Circular Plates Due to Asymmetric Temperature DistributionsChapter 5. Thermal Stresses in Beams and Circular Cylinders 5.1 Free Rectangular Beams 5.2 Free Beams of Arbitrary Cross-Section 5.3 Elementary Solutions for Free I-Beams 5.4 The End Problem in Free I-Beams 5.5 Thermal Deflections of Free Beams 5.6 Statically Indeterminate Beams (Externally Restrained) 5.7 Axisymmetric Thermal Stresses in Circular CylindersChapter 6. Thermal Stresses in Shells 6.1 Introduction 6.2 Shells of Arbitrary Shape 6.3 Shells of Revolution with a Meridian of Arbitrary Shape 6.4 Shells of Revolution of Constant Meridional Curvature 6.5 Circular Cylindrical Shells 6.5.1 Arbitrary Temperature Distributions 6.5.2 Radial and Circumferential Temperature Distributions 6.5.3 Axial Temperature Distributions 6.6 Discontinuity Problems in ShellsChapter 7. Thermal Buckling 7.1 Introduction 7.2 Columns or Bars 7.3 Thermal Buckling of Flat, Uniform Plates 7.3.1 Introduction 7.3.2 The Ritz-Galerkin Method 7.3.3 The Rayleigh-Ritz Method 7.3.4 Rectangular Plates 7.3.5 Circular Plates 7.4 Post-Buckling (Large Deflection) Analyses for Flat Plates 7.5 Thermal Buckling of Circular Cylindrical Shells 7.5.1 Radial Temperature Variations 7.5.2 Axial Temperature Variations 7.5.3 Circumferential Temperature Variations 7.6 Thermal Buckling of Thin Wings 7.6.1 General Instability 7.6.2 Local InstabilityChapter 8. Sundry Design Problems 8.1 Temperature-Dependent Material Properties 8.2 Optimum Design of Structures to Include Thermal Stress 8.2.1 Introduction 8.2.2 Optimum Thickness of a Plate Subjected to Normal Pressure and Temperature Variation through the Thickness 8.2.3 Optimum Design of a Multicell Box Subjected to a Given Bending Moment and Temperature Distribution 8.3. The Alleviation of Thermal Stress 8.3.1 Introduction 8.3.2 Thermal Insulation and Cooling 8.3.3 Elastic Insulation 8.4 Inelastic Thermal Stresses 8.5 Cyclic Thermal Loading: Incremental CollapseAppendix. Heat Transfer in Structures A.1 Heat Conduction A.2 Heat Convection A.2.1 Free Convection A.2.2 Forced Convection A.3 Heat Radiation A.4 Equilibrium Solutions A.5 Finite Difference Formulation of the Heat Transfer Problem A.5.1 The Heat Conduction Equation A.5.2 Boundary Conditions A.5.3 Some Typical FormulationsReferencesIndex