Theory of Matrix Structural Analysis

Overview


This pioneering aerospace engineering text belongs on the shelf of every aerospace and structural engineering graduate student and professional engineer. Originally published in 1968, the treatment remains a valuable guide, tracing each procedure in a clear, step-by-step fashion and employing minimal mathematical rigor in its examples.
The text begins with an overview of matrix methods and their application to the structural design of modern aircraft and aerospace vehicles. ...
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Overview


This pioneering aerospace engineering text belongs on the shelf of every aerospace and structural engineering graduate student and professional engineer. Originally published in 1968, the treatment remains a valuable guide, tracing each procedure in a clear, step-by-step fashion and employing minimal mathematical rigor in its examples.
The text begins with an overview of matrix methods and their application to the structural design of modern aircraft and aerospace vehicles. Subsequent chapters cover the basic equations of elasticity, energy theorems, structural idealization, Castigliano's theorem, derivation of stiffness matrices from flexibility, and constant-shear-flow panels. Additional subjects include a comparison of force and displacement methods, analysis of substructures, structural synthesis, and nonlinear structural analysis. Abundant end-of-chapter supplements provide materials for classroom use.
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Product Details

  • ISBN-13: 9780486649481
  • Publisher: Dover Publications
  • Publication date: 6/13/2012
  • Edition description: 46th EDITION, DOVER EDITION
  • Edition number: 46
  • Pages: 480
  • Sales rank: 1,034,280
  • Product dimensions: 5.40 (w) x 8.48 (h) x 0.96 (d)

Meet the Author

John Przemieniecki was a professor and Associate Dean for Research at the U.S. Air Force Institute of Technology and a member of the U.S. Senior Executive ServicePresident Reagan conferred upon him the rank of Distinguished Executive, and in 1999 he received an honorary doctorate from the Warsaw University of Technology.

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Table of Contents

PREFACE
CHAPTER 1 MATRIX METHODS
1.1 Introduction
1.2 Design Iterations
1.3 Methods of Analysis
1.4 Areas of Structural Analysis
CHAPTER 2 BASIC EQUATIONS OF ELASTICITY
2.1 Strain-Displacement Equations
2.2 Stress-Strain Equations
2.3 Stress-Strain Equations for Initial Strains
2.4 Equations of Equilbrium
2.5 Compatibility Equations
CHAPTER 3 ENERGY THEOREMS
3.1 Introduction
3.2 Work and Complementary Work; Stain Energy and Complementary Strain
3.3 Green's Identity
3.4 Energy Theorems Based on the Principle of Virtual Work
3.5 Energy Theorems Based on the Principle of Complementary Virtual Work
3.6 Clapeyron's Theorem
3.7 Betti's Theorem
3.8 Maxwell's Reciprocal Theorem
3.9 Summary of Energy Theorems and Definitions
  PROBLEMS
CHAPTER 4 STRUCTURAL IDEALIZATION
4.1 Structural Idealization
4.2 Energy Equivalence
4.3 Structural Elements
CHAPTER 5 STIFFNESS PROPERTIES OF STRUCTURAL ELEMENTS
5.1 Methods of Determining Element Force-Displacement Relationships
5.2 Determination of Element Stiffness Properties by the Unit-displacement Theorem
5.3 Application of Castigliano's Theorem (Part I) to Derive Stiffness Properties
5.4 Transformation of Coordinate Axes: ? Matrices
5.5 Pin-jointed Bar Elements
5.6 Beam Elements
5.7 Triangular Plate Elements (In-plane Forces)
5.8 Rectangular Plate Elements (In-plane Forces)
5.9 Quadrilateral Plate Elements (In-plane Forces)
5.10 Tetrahedron Elements
5.11 Triangular Plates in Bending
5.12 Rectangular Plates in Bending
5.13 Method for Improving Stiffness Matrices
  PROBLEMS
CHAPTER 6 THE MATRIX DISPLACEMENT METHOD
6.1 Matrix Formulation of the Displacement Analysis
6.2 Elimination of the Rigid-body Degrees of Freedom: Choice of Reactions
6.3 Derivation of the Transformation Matrix V from Equilibrium Equations
6.4 Derivation of the Transformation Matrix T from Kinematics
6.5 Condensation of Stiffness Matrices
6.6 Derivation of Stiffness Matrices from Flexibility
6.7 Stiffness Matrix for Constant-shear-flow Panels
6.8 Stiffness Matrix for Linearly Varying Axial-force Members
6.9 Analysis of a Pin-jointed Truss by the Displacement Method
6.10 Analysis of a Cantilever Beam by the Displacement Method
6.11 Equivalent Concentrated Forces
  PROBLEMS
CHAPTER 7 FLEXIBILITY PROPERTIES OF STRUCTURAL ELEMENTS
7.1 Methods of Determing Element Displacement-Force Relationships
7.2 Inversion of the Force-Displacement Equations: Flexibility Properties of Pin-jointed Bars and Beam Elements
7.3 Determination of Element Flexibility Properties by the Unit-load Theorem
7.4 Application of Castigliano's Theorem (Part II) to Derive Flexibility Properties
7.5 Solution of Differential Equations for Element Displacements to Derive Flexibility Properties
7.6 Pin-jointed Bar Elements
7.7 Beam Elements
7.8 Triangular Plate Elements (In-plane Forces)
7.9 Rectangular Plate Elements (In-plane Forces)
7.10 Tetrahedron Elements
7.11 Constant-shear-flow Panels
7.12 Linearly Varying Axial-force Members
7.13 Rectangular Plates in Bending
  PROBLEMS
CHAPTER 8 THE MATRIX FORCE METHOD
8.1 Matrix Formulation of the Unit-load Theorem for External-force Systems
8.2 Matrix Formulation of the Unit-load Theorem for Internal-force Systems: Self-equilibrating Force Systems
8.3 Matrix Formulation of the Force Analysis: Jordanian Elimination Technique
8.4 Matrix Force Analysis of a Pin-jointed Truss
8.5 Matrix Force Analysis of a Cantilever Beam
8.6 Comparison of the Force and Displacement Methods
  PROBLEMS
CHAPTER 9 ANALYSIS OF SUBSTRUCTURES
9.1 Substructure Analysis by the Matrix Displacement Method
9.2 Substructure Displacement Analysis of a Two-Bay Truss
9.3 Substructure Analysis by the Matrix Force Method
9.4 Substructure Force Analysis of a Two-bay Truss
  PROBLEMS
CHAPTER 10 DYNAMICS OF ELASTIC SYSTEMS
10.1 Formulation of the Dynamical Problems
10.2 Principle of Virtual Work in Dynamics of Elastic Systems
10.3 Hamilton's Principle
10.4 Power-Balance Equation
10.5 Equations of Motion and Equilibrium
10.6 Static and Dynamic Displacements in a Uniform Bar
10.7 Equivalent Masses in Matrix Analysis
10.8 Frequency-dependent Mass and Stiffness Matrices for Bar Elements
10.9 Frequency-dependent Mass and Stiffness Matrices for Beam Elements
  PROBLEMS
CHAPTER 11 INERTIA PROPERTIES OF STRUCTURAL ELEMENTS
11.1 Equivalent Mass Matrices in Datum Coordinate System
11.2 Equivalent Mass Matrix for an Assembled Structure
11.3 Condensed Mass Matrix
11.4 Pin-jointed Bar
11.5 Uniform Beam
11.6 Triangular Plate with Translational Displacements
11.7 Rectangular Plate with Translational Displacements
11.8 Solid Tetrahedron
11.9 Solid Parallelepiped
11.10 Triangular Plate with Bending Displacements
11.11 Rectangular Plate with Bending Displacements
11.12 Lumped-mass Representation
  PROBLEMS
CHAPTER 12 VIBRATIONS OF ELASTIC SYSTEMS
12.1 Vibration Analysis Based on Stiffness
12.2 Properties of the Eigenmodes: Orthogonality Relations
12.3 Vibration Analysis Based on Flexibility
12.4 Vibration of Damped Structural Systems
12.5 Critical Damping
12.6 Longitudinal Vibrations of an Unconstrained Bar
12.7 Longitudinal Vibrations of a Constrained Bar
12.8 Transverse Vibrations of a Fuselage-Wing Combination
12.9 Determination of Vibration Frequencies from the Quadratic Matrix Equation
  PROBLEMS
CHAPTER 13 DYNAMIC RESPONSE OF ELASTIC SYSTEMS
13.1 Response of a Single-degree-of-freedom System: Duhamel's Integrals
13.2 Dynamic Response of an Unconstrained (Free) Structure
13.3 Response Resulting from Impulsive Forces
13.4 Dynamic Response of a Constrained Structure
13.5 Steady-state Harmonic Motion
13.6 Duhamel's Integrals for Typical Forcing Functions
13.7 Dynamic Response to Forced Displacements: Response to Earthquakes
13.8 Determination of Frequencies and Modes of Unconstrained (Free) Structures Using Experimental Data for the Constrained Structures
13.9 Dynamic Response of Structural Systems with Damping
13.10 Damping Matrix Proportional to Mass
13.11 Damping Matrix Proportional to Stiffness
13.12 Matrix C Proportional to Critical Damping
13.13 Orthonormalization of the Modal Matrix p
13.14 Dynamic Response of an Elastic Rocket Subjected to Pulse Loading
13.15 Response Due to Forced Displacement at One End of a Uniform Bar
  PROBLEMS
CHAPTER 14 STRUCTURAL SYNTHESIS
14.1 Mathematical Formulation of the Optimization Problem
14.2 Structural Optimization
CHAPTER 15 NONLINEAR STRUCTURAL ANALYSIS
15.1 Matrix Displacement Analysis for Large Deflections
15.2 Geometrical Stiffness for Bar Elements
15.3 Geometrical Stiffness for Beam Elements
15.4 Matrix Force Analysis for Large Deflections
15.5 Inelastic Analysis and Creep
15.6 Stability Analysis of a Simple Truss
15.7 Stability Analysis of a Column
15.8 Influence of a Constant Axial Force on Transverse Vibrations of Beams
  PROBLEMS
APPENDIX A MATRIX ALGEBRA
APPENDIX B BIBLIOGRAPHY
INDEX
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