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Neil McCartney
Properties for Design of Composite Structures
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Страница 1
Properties for Design of Composite Structures Theory and Implementation Using Software
Страница 3
Contents
List of Figures
List of Tables
Guide
Pages
Preface
About the Companion Website
Страница 11
2 Fundamental Relations for Continuum Models
2.1 Introduction
2.2 Vectors
2.3 Tensors
2.3.1 Fourth-order Elasticity Tensors
2.4 Displacement and Velocity Vectors
2.5 Material Time Derivative
2.6 Continuity Equation
2.7 Equations of Motion and Equilibrium
2.8 Energy Balance Equation
2.8.1 Conservative Body Forces
2.9 Equations of State for Hydrostatic Stress States
2.9.1 Global Thermodynamic Relations
2.9.2 Local Thermodynamic Relations
2.10 Strain Tensor
2.11 Field Equations for Infinitesimal Deformations
2.12 Equilibrium Equations
2.13 Strain–Displacement Relations
2.14 Constitutive Equations for Anisotropic Linear Thermoelastic Solids
2.14.1 Isotropic Materials
2.15 Introducing Contracted Notation
2.16 Tensor Transformations
2.17 Transformations of Elastic Constants
2.17.1 Transverse Isotropic and Isotropic Solids
2.17.2 Introducing Familiar Thermoelastic Constants
2.18 Analysis of Bend Deformation
2.18.1 Geometry and Basic Equations
2.18.2 Stress and Displacement Fields
2.18.3 Some Special Cases
2.18.3.1 Four-point Bending Tests
2.18.3.2 Plane Strain Bending
References
3 Maxwell’s Far-field Methodology Applied to the Prediction of Effective Properties of Multiphase Isotropic Particulate Composites
3.1 Introduction
3.2 General Description of Maxwell’s Methodology Applied to Thermal Conductivity
3.2.1 Description of Geometry
3.2.2 Temperature Distribution for an Isolated Sphere Embedded in an Infinite Matrix
3.2.3 Maxwell’s Methodology for Estimating Conductivity
3.3 Bulk Modulus and Thermal Expansion Coefficient 3.3.1 Spherical Particle Embedded in Infinite Matrix Subject to Pressure and Thermal Loading
3.3.2 Applying Maxwell’s Methodology to Isotropic Multiphase Particulate Composites
3.4 Shear Modulus 3.4.1 Spherical Particle Embedded in Infinite Matrix Material Subject to Pure Shear Loading
3.4.2 Application of Maxwell’s Methodology
3.5 Summary of Results 3.5.1 Multiphase Composites
3.5.2 Two-phase Composites
3.6 Bounds for Two-phase Isotropic Composites
3.7 Comparison of Predictions with Known Results
References
4 Maxwell’s Methodology for the Prediction of Effective Properties of Unidirectional Multiphase Fibre-reinforced Composites Overview:
4.1 Introduction
4.2 General Description of Maxwell’s Methodology Applied to Thermal Conductivity
4.2.1 Temperature Distribution for an Isolated Fibre
4.2.2 Maxwell’s Methodology for Estimating Transverse Conductivity
4.3 The Basic Equations for Thermoelastic Analysis
4.3.1 Properties Defined from Axisymmetric Distributions
4.3.2 Solution for an Isolated Fibre Perfectly Bonded to the Matrix
4.3.3 Solution in the Absence of Fibre
4.3.4 Applying Maxwell’s Approach to Multiphase Fibre Composites
4.4 Axial Shear of Anisotropic Fibres
4.4.1 Solution for an Isolated Fibre Perfectly Bonded to the Matrix
4.4.2 Solution in the Absence of Fibre
4.4.3 Applying Maxwell’s Approach to Multiphase Fibre Composites
4.5 Transverse Shear of Multiphase Fibre Composites
4.5.1 Representation for Displacement Strain and Stress Distributions
4.5.2 Stress Field in the Absence of Fibre
4.5.3 Displacement and Stress Fields in Fibre
4.5.4 Displacement and Stress Fields in Matrix
4.5.5 Applying Maxwell’s Approach to Multiphase Fibre Composites
4.6 Other Effective Elastic Properties for Multiphase Fibre-reinforced Composites
4.7 Relationship between Two-phase and Multiphase Formulae
4.8 Summary of Results for Multiphase Composites
4.9 Results for Two-phase Fibre-reinforced Composites
4.10 Bounds for Two-phase Fibre-reinforced Composites
4.10.1 Thermal Conductivity
4.10.2 Axial Young’s Modulus
4.10.3 Axial Poisson’s Ratio
4.10.4 Transverse Bulk Modulus
4.10.5 Transverse Shear Modulus
4.10.6 Axial Shear Modulus
4.10.7 Axial Thermal Expansion
4.10.8 Transverse Thermal Expansion
4.11 Comparison of Predictions with Known Results
References
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