Theory of Matrix Structural Analysis

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9780486649481: Theory of Matrix Structural Analysis

This classic text begins with an overview of matrix methods and their application to the structural design of modern aircraft and aerospace vehicles. Subsequent chapters cover basic equations of elasticity, energy theorems, structural idealization, a comparison of force and displacement methods, analysis of substructures, structural synthesis, nonlinear structural analysis, and other topics. 1968 edition.

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About 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 Service. President Reagan conferred upon him the rank of Distinguished Executive, and in 1999 he received an honorary doctorate from the Warsaw University of Technology.

Contenuti:

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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Przemieniecki, J. S.
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