- Артикул:00-01050861
- Автор: Bruce K. Donaldson
- ISBN: 978-0-521-86583-8
- Обложка: Твердая обложка
- Издательство: Cambridge University Press (все книги издательства)
- Город: New York
- Страниц: 974
- Год: 2008
- Вес: 2577 г
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Книга на английском языке.
As with the first edition, this textbook provides a clear introduction to the fundamental theory of structural analysis as applied to vehicles, aircraft, spacecraft, automobiles, and ships. The emphasis is on the application of fundamental concepts of structural analysis in everyday engineering practice. No assumptions are made with regard to the method of analysis. All approximations are accompanied by a full explanation of their validity. Repetition is an important learning tool, and so some redundancy appears to dispel misunderstanding. The number of topics covered in detail is limited to those essential for modern structural engineering practice. In this new edition, more topics, figures, examples, and exercises have been added. A primary change has been a greater emphasis on the finite element methods of analysis. Three new chapters are now included, and clarity remains the hallmark of this text.
Contents
Introduction to the Second Edition
Introduction to the First Edition
List of Repeated Engineering Symbols
Acknowledgments
Part I The Fundamentals of Structural Analysis
I.1 An Overview of Part I
I.2 Summary of Taylor’s Series
I.3 Summary of Newton’s Method for Finding Roots
I.4 The Binomial Series
I.5 The Chain Rule for Partial Differentiation
1 Stress in Structures
1.1 The Concept of Stress
1.2 The General Interior Equilibrium Equations
1.3 Equilibrium at the Outer or Inner Boundary
1.4 Plane Stress
1.5 Summary
Chapter 1 Exercises
2 Stresses and Coordinate Axis Rotations
2.1 Introduction
2.2 Stress Values in Other Cartesian Coordinate Systems
2.3 The Determination of Maximum Stress Values
2.4 Mohr’s Circle
2.5 A Three-Dimensional View of Plane Stress
2.6 **Principal Stresses in the General Three-Dimensional Case**
2.7 Summary
2.8 Octahedral (von Mises) Shearing Stresses
2.9 **The Mathematical Description of Stresses**
Chapter 2 Exercises
Endnote (1) Solution for the Planes of Principal Stress
3 Displacements and Strains
3.1 Introduction
3.2 Displacements
3.3 Longitudinal Strains
3.4 Shearing Strains
3.5 Other Strain Definitions
3.6 The Strain-Displacement Equations
3.7 The Compatibility Equations
3.8 Plane Strain
3.9 Summary
Chapter 3 Exercises
Endnote (1) The Derivation of the Strain-Displacement Equations
for Cylindrical Coordinates
Endnote (2) A Third Derivation of the Compatibility Equations
4 Strains in Rotated Coordinate Systems
4.1 Introduction
4.2 Strains in Other Cartesian Coordinate Systems
4.3 Strain Gauges
4.4 The Mathematical Properties of Strains
4.5 Summary
Chapter 4 Exercises
5 The Mechanical Behavior of Engineering Materials
5.1 Introduction
5.2 The Tensile Test
5.3 Compression and Shear Tests
5.4 Safety Factors
5.5 Factors Other than Stress That Affect Material Behavior
5.6 **Biaxial and Triaxial Loadings**
5.7 Simplifications of Material Behavior
Chapter 5 Exercises
Endnote (1) Residual Stress Example Problem
Endnote (2) Crack Growth Example
6 Linearly Elastic Materials
6.1 Introduction
6.2 Orthotropic Materials
6.3 Isotropic and Other Linearly Elastic Materials
6.4 The Plane Stress Constitutive Equations
6.5 **Applications to Fiber Composites**
6.6 Summary
Chapter 6 Exercises
Endnote (1) Negative Poisson Ratios
Part II **Introduction to the Theory of Elasticity**
II.1 Introduction
7 The Theory of Elasticity
7.1 Introduction
7.2 A Theory of Elasticity Solution Using Stresses
7.3 A Theory of Elasticity Solution Using Displacements
7.4 Reprise
7.5 Summary
Chapter 7 Exercises
Endnote (1) General Problem Formulations
Endnote (2) Another Solution to the Disk Displacement Equation
Endnote (3) Example 7.1 Compatibility Equation
8 Plane Stress Theory of Elasticity Solutions
8.1 Introduction
8.2 Solution Examples
8.3 St. Venant’s Principle
8.4 **Review Problem**
8.5 Summary
8.6 **The Airy Stress Function**
Chapter 8 Exercises
Endnote (1) An Example of Calculating Displacements
from a Stress Solution
Parts I and II Review Questions
Part III Engineering Theory for Straight, Long Beams
III.1 Aircraft and Other Vehicular Structures
III.2 The Method of Undetermined Coefficients
III.3 Linear Independence
III.4 The Mean Value Theorem
9 Bending and Extensional Stresses in Beams
9.1 Introduction
9.2 An Elaboration on the Scope of Strength of Materials
9.3 Stress Resultants
9.4 The Approximate Pattern for Beam Displacements
9.5 The Accuracy of the Beam Stress Equation
9.6 Calculation of the Area Properties of the Nonhomogeneous
Cross-Section
9.7 Calculation of Equivalent Thermal Loads
9.8 Principal Axes for the Beam Cross-Section
9.9 Summary
Chapter 9 Exercises
Endnote (1) The Predominance of the Normal Axial Stress
Endnote (2) Schwartz’s Inequality
10 Beam Bending and Extensional Deflections
10.1 Introduction
10.2 The Small Deflection Beam Equilibrium Equations
10.3 Nonlinear Beam Equilibrium Equations
10.4 Boundary Conditions and the Boundary Value
Problem
10.5 Uncoupled Forms of the GDEs and the BCs
10.6 Solutions for Beam Deflection Problems
10.7 Summary
Chapter 10 Exercises
Endnote (1) Different BCs in Different Planes at the Same Beam End
Endnote (2) The Nonlinear Form of the Axial Deflection Equation
Endnote (3) The Presence of the Moment per Unit Length Terms in the Shear
Force Boundary Condition Expressions
Endnote (4) Exact Integrations for a Nonuniform Beam
11 Additional Beam Bending Topics
11.1 Introduction
11.2 The Concept of Elastic Boundary Conditions
11.3 Elastic Support Boundary Conditions
11.4 Concentrated and Partial Span Loads
11.5 Partial Span and Concentrated Load Example Problems
11.6 Introduction to Beam Buckling
11.7 **Additional Comments on Beam Buckling**
11.8 Summary
Chapter 11 Exercises
Endnote (1) The Bending Slope Sign Convention
Endnote (2) Combined Beam Axial and Lateral Loadings
Endnote (3) Heaviside Step Function Additional Comments
Endnote (4) Combined Bending and Torsional Loadings
Endnote (5) Beams Continuous over Several Supports
12 Uniform Torsion of Beams
12.1 Introduction
12.2 The Stress Formulation for Uniform Torsion
12.3 Further Properties of the Prandtl Stress Function
12.4 The Membrane Analogy
12.5 Closed Form Beam Torsion Analytical Solutions
12.6 Open Form Uniform Beam Torsion Solutions
12.7 Summary
Chapter 12 Exercises
Endnote (1) A Comment on the Solution for a Circular Shaft with a Keyway
Endnote (2) Orthogonality
Endnote (3) A Separation of Variables Approach to Example 12.1
13 Beam Torsion Approximate Solutions
13.1 Introduction
13.2 Open Cross-Section Beam Torsion
13.3 Closed Section Beam Torsion
13.4 Accuracy of the Uniform Torsion Theory
13.5 Beams Subjected to a Variable Torque
13.6 Summary
Chapter 13 Exercises
Endnote (1) Torsion Constants for Rolled and Extruded Beams
Endnote (2) Warping Constraint Due to Varying Torque
Beam Bending and Torsion Review Questions
14 Beam Shearing Stresses Due to Shearing Forces
14.1 Introduction
14.2 Thin-Walled Open Cross-Sections
14.3 Thin-Walled Open Cross-Section Example Problems
14.4 The Open Section Shear Center
14.5 Shear Flows in Thin-Walled Closed Cross-Sections
14.6 Summary
Chapter 14 Exercises
Endnote (1) The Shear Center as the Center of Twist
Part IV Work and Energy Principles
IV.1 Preface
IV.2 The Green-Gauss Theorem
15 Work and Potential Energy Principles
15.1 Introduction
15.2 Work and Potential Energy
15.3 Virtual Work and Virtual Potential Energy
15.4 The Variational Operator
15.5 The Principle of Virtual Work
15.6 Internal Virtual Work
15.7 Complementary Virtual Work
15.8 **Energy and Other Principles**
15.9 **Modifications for Temperature Changes**
15.10 Summary
Chapter 15 Exercises
Endnote (1) Further Explanation of the Variational Operator
Endnote (2) Proof That the Principle of Virtual Work Is a Sufficient
Condition for Equilibrium
Endnote (3) Proof of the Pairing of BCs for the Beam Fourth Order Bending
Equations and the Second Order Extension Equations
Endnote (4) Derivation of the Uniform Torsion Beam Equations Using the
Principle of Complementary Virtual Work
Part V Energy-Based Numerical Solutions
V.1 Preface
16 **Precursor Numerical Analyses**
16.1 Introduction
16.2 Numerical Methods of Note
16.3 Summary
Chapter 16 Exercises
17 Introduction to the Finite Element Method
17.1 Introduction
17.2 Generalized Coordinates
17.3 The Beam Bending Finite Element
17.4 The Bar and Spring Element Stiffness Matrix Equations
17.5 Assembling the System Matrix Equation
17.6 Solving the System Matrix Equation
17.7 Example Beam Frame and Grid Problems
17.8 More Extensive Example Problems
17.9 Summary
Chapter 17 Exercises
Endnote (1) Distributed Coordinates
Endnote (2) Accuracy of the Concentrated Load Approximation
Endnote (3) The Reason for the Name “Generalized Coordinates”
18 Finite Element Truss Problems
18.1 Introduction
18.2 The Rotated Bar Element
18.3 Equivalent Thermal Loads
18.4 Other Initial Strains
18.5 Enforced Deflections
18.6 Summary
Chapter 18 Exercises
Endnote (1) Substructuring in Static Analyses
19 Basic Aspects of Multidimensional Finite Elements
19.1 Introduction
19.2 A Rectangular Plane Stress Finite Element
19.3 A Triangular Plane Stress Element in Brief
19.4 Three-Dimensional Finite Elements
19.5 Refined Finite Elements of Simple Shapes
19.6 **The Finite Element Method with Time-Varying Loads**
19.7 Summary
Chapter 19 Exercises
Endnote (1) An Explanation for Rigid Body Motion-Induced False Strains
Endnote (2) Reducing the Number of DOF in a Dynamic Analysis
20 The Unit Load Method for Determinate Structures
20.1 Introduction
20.2 External Complementary Virtual Work in the Unit Load Method
20.3 Internal CVW for Beam Bending and Extension
20.4 Internal Complementary Virtual Work for Beam Torsion
20.5 **Internal CVW for Beam Shearing**
20.6 Additional Illustrative Examples
20.7 **Examples of Using the ULM for Design Purposes**
20.8 **General Deflection Solutions**
20.9 **Large Radius Curved Beams**
20.10 Summary
20.11 Maxwell’s Reciprocity Theorem
Chapter 20 Exercises
Endnote (1) ULM Limitations
Endnote (2) Internal Complementary Virtual Work
21 The Unit Load Method for Indeterminate Structures
21.1 Introduction
21.2 Identifying Redundant Forces and Moments
21.3 The Coiled Spring Structural Elements
21.4 The Strategy of Releases and Reattachments
21.5 Example Problems
21.6 **Further Example Problems**
21.7 Summary
Chapter 21 Exercises
Parts IV and V Review Questions
Part VI Thin Plate Theory and Structural Stability
VI.1 Introduction
22 Thin Plate Theory
22.1 Introduction
22.2 The Plate Midplane
22.3 The Plate Stress Resultants
22.4 The Approximate Pattern for Plate Displacements
22.5 The Small Deflection Thin Plate Bending Equation
22.6 Thin Plate Boundary Conditions
22.7 **Classical Small Deflection Plate Bending Solutions**
22.8 **Plate Buckling and Its Uses**
22.9 A Simple Plate Bending Finite Element
22.10 Summary
Chapter 22 Exercises
Endnote (1) The Second Finite Deflection Plate Equation
23 Elastic and Aeroelastic Instabilities
23.1 Introduction
23.2 An Energy Formulation of the Beam Buckling Problem
23.3 A Beam Buckling Finite Element
23.4 Further Aspects of the Energy Formulation
23.5 Types of Fluid-Structure Interaction Instabilities
23.6 Airfoil Divergence
23.7 Airfoil Flutter
23.8 Matrix Iteration for Symmetric Matrices
Chapter 23 Exercises
Endnote (1) Resonance
Endnote (2) Diagonalization and Functions of Matrices
Appendix A: Additional Topics
A.1 Integration of the Strains to Obtain Displacements
A.2 Proof of the Symmetry of the Compliance Matrix
A.3 Uniform Torsion Stress Resultants for Multiply Connected
Cross-Sections
A.4 The Uniform Torsion GDE for Multiply Connected Cross-Sections
A.5 Calculation of the Twist per Unit Length of a Single Cell of an N-Cell
Cross-Section
Appendix B: Selected Answers to Exercises
References
Index
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