Thermal Stress Analyses

Thermal Stress Analyses

1st Edition - January 1, 1965

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  • Author: D. J. Johns
  • eBook ISBN: 9781483227047

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Thermal Stress Analyses deals with both elastic and plastic thermal stresses produced from large variations in temperature and thermal expansion in materials whose properties are time-independent. This book is composed of eight chapters. The opening chapter illustrates the general three-dimensional thermoelastic problem, which requires the determination of stress, strains and displacements, when the body forces and boundary conditions are known while the next chapter demonstrate a simpler, two-dimensional formulation involving plane strain and plane stress. The succeeding five chapters describe thermal stresses in various structures, including in thin plates, beams, circular cylinders, and shells. The closing chapters consider the mechanism of thermal buckling and sundry design problems. This book is of value to mechanical engineers, and to mechanical engineering teachers and students.

Table of Contents

  • Preface


    Principal Notation

    Chapter 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 Solution

    Chapter 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 Plates

    Chapter 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 Distributions

    Chapter 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 Cylinders

    Chapter 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 Shells

    Chapter 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 Instability

    Chapter 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 Collapse

    Appendix. 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 Formulations



Product details

  • No. of pages: 230
  • Language: English
  • Copyright: © Pergamon 2013
  • Published: January 1, 1965
  • Imprint: Pergamon
  • eBook ISBN: 9781483227047

About the Author

D. J. Johns

About the Editor

B. G. Neal

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