Analysis of Engineering Structures and Material Behavior

Title Page

Copyright

Contents

Frequently Used Symbols and the Meaning of Symbols

Principal SI Units and the US Equivalents

SI Prefixes, Basic Units, Physical Constants, the Greek Alphabet

Important Notice Before Reading the Book

Preface

About the Author

Acknowledgements

Chapter 1 Introduction

1.1 The Task of Design and Manufacture

1.2 Factors that Influence the Design of Engineering Structures

1.3 The Importance of Optimization in the Process of Design and the Selection of Structural Materials

1.4 Commonly Observed Failure Modes in Engineering Practice

1.5 Structures and the Analysis of Structures

References

Chapter 2 Stress

2.1 Definition of Average Stress and Stress at a Point

2.2 Stress Components and Equilibrium Equations

2.2.1 Stress Components

2.2.2 Equilibrium Equations

2.3 Stress Tensor

2.3.1 Mean and Deviatoric Stress Tensors

2.4 States of Stress

2.4.1 Uniaxial State of Stress

2.4.2 Two-dimensional State of Stress

2.4.3 Three-dimensional State of Stress

2.4.3.1 Stress on an Arbitrary Plane

2.4.3.2 Stress on an Octahedral Plane

2.4.3.3 Principal Stresses and Stress Invariants

2.5 Transformation of Stress Components

References

Chapter 3 Strain

3.1 Definition of Strain

3.1.1 Some Properties of Materials Associated with Strain

3.1.1.1 Poisson´s Ratio

3.1.1.2 Volumetric Strain

3.1.1.3 Bulk Modulus

3.1.1.4 Modulus of Elasticity

3.1.1.5 Shear Modulus (Modulus of Rigidity)

3.2 Strain–Displacement Equations

3.3 Strain Tensors

3.3.1 Small Strain Tensor

3.3.2 Finite Strain Tensor

3.3.3 Mean and Deviatoric Strain Tensors

3.3.4 Principal Strains and Strain Invariants

3.3.4.1 Strain Tensor

3.3.4.2 Deviatoric Strain Tensor

3.4 Transformation of Strain Components

3.4.1 Mohr´s Circle

3.5 Strain Measurement

References

Chapter 4 Mechanical Testing of Materials

4.1 Material Properties

4.2 Types of Material Testing

4.3 Test Methods Related to Mechanical Properties

4.4 Testing Machines and Specimens

4.4.1 Static Tensile Testing Machine and Specimens

4.4.2 Impact Testing Machine and Specimens

4.4.3 Hardness Testing Machine

4.4.4 Fatigue Testing Machines

4.5 Test Results

4.5.1 Static Tensile Test Results

4.5.1.1 Engineering Stress–Strain Diagram

4.5.1.2 Creep Diagram/Curve

4.5.1.3 Relaxation Diagram/Curve

4.5.2 Dynamic Test Results

4.5.2.1 Tensile, Flexural and Torsional Test Results

4.5.2.2 Toughness Test Results

4.5.2.3 Fracture Toughness Test Results

References

Chapter 5 Material Behavior and Yield Criteria

5.1 Elastic and Inelastic Responses of a Solid

5.2 Yield Criteria

5.2.1 Ductile Materials

5.2.1.1 Maximum Shear Stress Criterion (Tresca Criterion)

5.2.1.2 Distortional Energy Density Criterion (von Mises Criterion)

5.2.2 Brittle Materials

5.2.2.1 Maximum Normal Stress Criterion

5.2.2.2 Maximum Normal Strain Criterion

References

Chapter 6 Loads Imposed on Engineering Elements

6.1 Axial Loading

6.1.1 Normal Stress

6.1.2 The Principal Stress

6.2 Torsion

6.2.1 Elastic Torsion – Shear Stress and Strain Analysis

6.2.1.1 Prismatic Bars: Circular Cross-section

6.2.1.2 Prismatic Bars: Noncircular Cross-section

6.2.1.3 Thin-walled Structures

6.2.2 Warping (Distortion) of a Cross-section

6.2.3 Inelastic Torsion and Residual Stress

6.2.3.1 Residual Stress

6.3 Bending

6.3.1 Beam Supports, Types of Beams, Types of Loads

6.3.2 Internal Forces – Bending Moments (Mf), Shear Force (Q), Distributed Load (q)

6.3.3 Principal Moments of Inertia of an Area (I1, I2) and Extreme Values of Product of Inertia (Ixy) of an Area

6.3.3.1 Axes Parallel to the Centroidal Axes

6.3.3.2 Rotation of the Coordinate Axes at the Observed Point (Rotated Axes)

6.3.4 Symmetrical Bending

6.3.4.1 Pure Bending

6.3.4.2 Nonuniform Bending

6.3.5 Nonsymmetrical Bending

6.3.6 Loading of Thin-walled Engineering Elements; Shear Center

6.3.6.1 Shear Center

6.3.7 Beam Deflections

6.3.8 Bending of Curved Elements

6.4 Stability of Columns

6.4.1 Critical Buckling Force in the Elastic Range

6.4.1.1 Pin-ended Columns

6.4.1.2 Columns with Other End Conditions

6.4.2 Critical Buckling Stress in the Elastic Range

6.4.3.1 Local Buckling of the Column

6.5 Eccentric Axial Loads

6.5.1 Eccentric Axial Load Acting in a Plane of Symmetry

6.5.2 General Case of an Eccentric Axial Load

References

Chapter 7 Relationships Between Stress and Strain

7.1 Fundamental Considerations

7.2 Anisotropic Materials

7.3 Isotropic Materials

7.3.1 Determination of Hooke´s Law – Method of Superposition

7.3.2 Engineering Constants of Elasticity

7.4 Orthotropic Materials

7.5 Linear Stress–Strain–Temperature Relations for Isotropic Materials

References

Chapter 8 Rheological Models

8.1 Introduction

8.2 Time-independent Behavior Modeling

8.2.1 Elastic Deformation Modeling

8.2.1.1 Hooke´s Element (H Model)

8.2.2 Deformation Modeling after the Elastic Limit

8.2.2.1 Saint Venant Element (SV Model)

8.2.2.2 Saint Venant Element–Spring/(SV–Spring)

8.2.2.3 Saint Venant Element | Spring-Spring/(SV | Spring-Spring)

8.3 Time-dependent Behavior Modeling

8.3.1 Newton Element (N Model): Linear Viscous Dashpot Element

8.3.2 Maxwell Model (M=H-N)

8.3.2.1 Generalized Maxwell Model

8.3.3 Voigt-Kelvin Model (K=H | N)

8.3.3.1 Generalized Voigt–Kelvin Model

8.3.4 Standard Linear Solid Model (SLS)

8.3.5 Voigt–Kelvin-Hooke´s Model (K-H)

8.3.6 Burgers´ Model

8.4 Differential Form of Constitutive Equations

References

Chapter 9 Creep in Metallic Materials

9.1 Introduction

9.2 Plastic Deformation – General

9.2.1 Slip

9.2.2 Cleavage

9.2.3 Twinning

9.2.4 Grain Boundary Sliding

9.2.5 Void Coalescence

9.3 The Creep Phenomenon and Its Geometrical Representation

9.3.1 Creep Deformation Maps and Fracture Mechanism Maps

9.3.1.1 Creep Deformation Mechanisms

9.3.1.2 Fracture Micromechanisms and Macromechanisms

9.3.1.3 Creep Fracture Mechanisms

9.3.2 Short-time Uniaxial Creep Tests, Creep Modeling and Microstructure Analysis

9.3.2.1 Short-time Uniaxial Creep Tests

9.3.2.2 Creep Modeling

9.3.2.3 Microstructure Analysis – Basic

9.3.3 Long-term Creep Behavior Prediction Based on the Short-time Creep Process

9.3.3.1 Extrapolation Methods

9.3.3.2 Time–Temperature Parameters

9.3.4 Multiaxial Creep

9.4 Relaxation Phenomenon and Modeling

References

Chapter 10 Fracture Mechanics

10.1 Introduction

10.2 Fracture Classification

10.3 Fatigue Phenomenon

10.3.1 Known Starting Points

10.3.2 Stress versus Life Curves (?–N/S–N), Endurance Limit

10.4 Linear Elastic Fracture Mechanics (LEFM)

10.4.1 Basic Consideration

10.4.2 Crack Opening Modes

10.4.2.1 Stress Intensity Factor (K/SIF)

10.4.2.2 Plastic Zone Size around the Crack Tip

10.4.2.3 Plastic Zone Shape around the Crack Tip

10.5 Elastic–Plastic Fracture Mechanics (EPFM)

10.5.1 The J Integral

10.6 Experimental Determination of Fracture Toughness

10.6.1 Test Specimens: Shapes, Dimensions, Orientations and Pre-cracking

10.6.1.1 Shapes and Dimensions of the Specimens

10.6.1.2 Orientation of a Specimen Made from Base Material

10.6.1.3 Fatigue Pre-cracking

10.6.2 Fracture Toughness, KIc and the K–R Curve

10.6.2.1 R-curve (K–R Curve)

10.6.2.2 Plane Strain Fracture Toughness (KIc) Testing

10.6.3 Fracture Toughness JIc and the J–R Curve

10.6.3.1 R-curve (J–R Curve)

10.6.3.2 Fracture Toughness (JIc) Determination/Testing

10.7 Charpy Impact Energy Testing

10.8 Crack Propagation

10.8.1 Introduction

10.8.2 Fatigue Crack Growth

10.8.2.1 The Paris Equation

10.8.2.2 The Walker Equation

10.8.2.3 The Forman Equation

10.8.2.4 The Forman–Newman–de Koning Equation

10.8.3 Creep Crack Growth

10.8.4 Life Assessment of Engineering Components

10.8.4.1 Constant Amplitude Loading

10.8.4.2 Variable Amplitude Loading

10.8.5 Crack Closure

10.8.5.1 Elber Crack Closure Phenomenon

10.8.6 A Brief Review of Testing of Unnotched, Axially Loaded Specimens

References

Chapter 11 The Finite Element Method and Applications

11.1 The Finite Element Method (FEM) in the Analysis of Engineering Problems

11.1.1 Applications of FEM

11.1.2 The Advantages of Using the FEM

11.1.3 A Brief Overview of the Historical Development of the FEM

11.2 Linear Analysis of Structural Behavior

11.2.1 Formulations of Equilibrium Equations

11.2.1.1 Variational Formulation of the Finite Element (Equilibrium) Equation

11.2.2 Structures

11.2.3 Finite Elements

11.2.4 Shape Functions – Cartesian and Natural (Dimensionless) Coordinate Systems

11.2.4.1 Cartesian Coordinate System

11.2.4.2 Natural (Dimensionless) Coordinate System

11.2.5 One-dimensional Finite Elements

11.2.5.1 Basic 1-D Finite Elements

11.2.5.2 Finite Elements of Higher Order

11.2.6 Two-dimensional Finite Elements

11.2.6.1 Basic 2-D Finite Elements

11.2.6.2 Finite Elements of Higher Order

11.2.6.3 Transformation Procedure for the Finite Element Equation

11.2.7 Three-dimensional Finite Elements

11.2.7.1 Basic 3-D Finite Elements

11.2.7.2 Finite Elements of Higher Order

11.2.8 Isoparametric Finite Elements

11.2.8.1 Introduction

11.2.8.2 Isoparametric Representation

11.2.9 Bending of Elastic Flat Plates

11.2.9.1 Deformation Theories for Elastic Plates

11.2.9.2 Finite Elements Based on Kirchhoff Plate Theory

11.2.10 Basics of Dynamic Behavior of Elastic Structures

11.2.10.1 Mass Matrix of the Finite Element

11.2.10.2 Free, Undamped Vibrations of Constructions – Eigenvalues

11.3 A Brief Introduction to Nonlinear Analysis of Structural Behavior

11.4 Metal-forming Processes – Brief Overview

11.4.1 Introduction

11.4.2 Classification, Variables and Characteristics of Metal-forming Processes

11.4.2.1 Comparison of Hot and Cold Working Processes in Terms of Working Temperature, Shaping Force and Achieved Material ...

11.4.3 Basic Settings Related to the Theory of Metal-forming Processes

11.4.3.1 Strain-rate Tensor and Data Relating to Yield Criteria

11.4.3.2 Virtual Work-rate Principle

11.4.3.3 The Prandtl–Reuss Equations

11.4.3.4 The Governing Equations of Plastic Deformation

11.4.3.5 Shape Functions

11.4.3.6 Strain-rate Matrix

11.5 The Application of the Finite Element Method in Structural Analysis

11.5.1 One-dimensional Finite Elements: Finite Element Analysis of Truss Structure Deformation

11.5.2 Two-dimensional Finite Elements: J Integral Calculation

11.5.3 Special Two-dimensional Finite Elements in Shear Stress Analysis

11.5.3.1 Introduction

11.5.3.2 Application of General Quadrilateral Finite Elements

References

Index

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