《Virtual Principles in Aircraft Structures：Volume 1: Analysis》
《Virtual Principles in Aircraft Structures：Volume 1: Analysis》飞机结构的虚拟原理：第1卷：分析
作者：
B.E. GATEWOOD
Professor Emeritw, Dept. of Aeronautical and Astronautical Engineering,
The Ohio State University, Columbw, Ohio, U.S.A.
出版社：Kluwer
出版时间：1989年
目录
]Preface xill
Chapter 1 / The basic three, two, and one dimensional equations
.in structural analysis 1
1.1 Introduction
1.2 Three diIJ1ensional equations
1.3 The displacement method of solution
1.4 The stress method of solution
1.5 The combined method of solution
1
2
6
7
8
1.6 Two dimensional equations 8
1. 7 Saint Venant's principle 10
1.8 One dimensional beam equations 11
1.9 No shear stresses in the beam 13
1.10 Beam cross section of a thin plate with one shear stress 13
1.11 Thin web beams with, large flange areas and one shear stress 17
1.12 Torsion of circular cross section and thin wall closed box 18
1.13 Thin web box beam with general loading 20
1.14 Inelastic effects in beams with temperature 21
1.15 Example of inelastic axial stresses and strains with temperature 25
1.16 Sequence loading and thermal cycling in beams 27
1.17 Load-strain design curves for beams 31
1.18 Problems 33
References 35
Chapter 2 / Virtual displacement and virtual force methods in
structural analysis 37
2.1 Introduction 37
2.2 The principle of virtual displacements
2.3 The unit displacement theorem
2.4 The principle of virtual forces
39
41
43
vi Oontents of Volume 1: Analysis
2.5 The unit load theorem 45
2.6 The principle of mixed virtual stresses and virtual displacements 46
2.7 The mixed unit displacement and unit load theorem 47
2.8 Two dimensional form of the virtual principles 48
2.9 One dimensional forms of the virtual principles 49
2.10 The one dimensional virtual principles with temperature, inelastic
and large displacement effects 54
2.11 Matrix forms of the virtual principles 56
2.12 Problems 59
References 61
Ch~pter 3 / The virtual principles for pin-jointed trusses 62
3.1 Introduction 62
3.2 The unit displacement theorem for trusses 64
3.3 The unit load theorem for trusses 70
3.4 Inelastic effects with temperature changes in trusses 74
3.5 Matrix equations for trusses. from the unit displacement theorem 81
3.6 Matrix equations for trusses from the unit load theorem 87
3.7 Matrix equations for trusses from the mixed unit displacement and
unit load theorem 96
3.8 Problems 98
References 102
Chapter 4 / The virtual principles for simple beams 103
4.1 Introduction 103
4.2 Principle of virtual displacements for beams 104
4.3 Point values for beam elements by the principle of virtual displacements
108
4.4 Principle of virtual forces for beams 114
4.5 Point values for beam elements by the unit load theorem 119
4.6 ,Principle of mixed virtual stresses and virtual displacements for
beams 122
4.7 Inelastic and temperature effects in simple beams 123
4.8 Matrix equations for beams from the unit displacement theorem 130
4.9 Matrix equations for beams from the unit load theorem 136
4.10 Matrix equations for beams from the mixed unit displacement and
unit load theorem 145
4.11 The beam colump equations 147
4.12 Problems 149
References 152
Chapter 5 / Box beam shear stresses and deflections 153
5.1 Introduction 153
5.2 Shear stresses in beams 154
Oontent! of Volume 1: Analysis vii
5.3 Torsional shear stresses in beams 158
5.4 Shear flows in open box beams 160
5.5 Shear flows in single cell box beams 163
5.6 Shear flows in multi-cell box beams 165
5.7 Shear center for closed box beams 168
5.8 Shear flows in tapered box beams 170
5.9 Inelastic and buckling shear stresses in beams 173
5.10 Axial and bending deflections of box beams with inelastic and
temperature effects 174
5.11 Shear deflections of beams 177
5.12 Torsional rotation of beams 183
5.13 Rota$ion of swept wings 189
5.14 Span~ise airload distribution and static wing divergence under
rotation 190
5.15 Static aileron effectiveness and reversal speed under wing rotation 195
5.16 Problems 199
References 201
Chapter 6 / Shear lag in thin web structures 202
6.1 Introduction 202
Part 1. Solutions for determinate cases 203
6.2 Shear flows due to concentrated loads into thin webs 203
6.3 Shear flows around cut-outs in thin web beams 206
6.4 Cut-outs in box beams 208
6.5 Shear flows in ribs and bulkheads 210
6.6 Forces on ribs due to airloads and taper effects 214
Part B. Solutions for redundant cases 216
6.7 Restraint effects in thin web structures 216
6.8 Shear flows in redundant beams in one plane 216
6.9 Deflections of thin w:eb structures 226
6.10 Flexibility matrices for shear web elements and stiffener elements 231
6.11 Matm solutions for thin web beams in one plane 233
6.12 Matrix solutions for box beams 241
6.13 Load redistribution in swept back wings 248
6.14 Problems 250
References 252
Appendix A / Notes on matrix algebra 254
A.1 Definition of matrices 254
A.2 Addition, subtraction, multiplication of matrices 255
A.3 Determinants 256
A.4 Matrix inversion 257
A.5 Solution of systems of simultaneous equations by matrices 260
A.6 Solution of systems of simultaneous equation,s by tri-diagonal
matrices 261
viii Oontents of Volume 1: Analysis
A.7 Solution of systems of equations by Jordan successive
transformations
A.8 Matrix representations
A.9 Orthogonal matrices
A.10 Eigenvalues and eigenvectors of matrices
A.11 Note on matrix notation
References
Appendix B / External forces on Hight vehicles
265
267
270
275
276
277
279
B.1 Introduction 279
B.2 \ Inertial forces for rigid body translation and rotation in a vertical
plane 281
B.3 Air forces on airplane wing 285
B.4 Airplane equilibrium equations in flight. Load factors 287
B.5 Velocity-load factor (V -n) diagram for design 289
B.6 Wing spanwise lift coefficient distribution 292
B.7 Spanwise lift coefficient distribution on twisted wings 295
B.8 Spanwise airload, shear, and moment distributions on wing 297
B.9 Distribution of inertia forces on wing and fuselage 301
B.10 Forces and moments on landing gear structures 304
B.11 Thermal forces 308
B.12 Miscellaneous forces 310
B.13 Deflection effects on the external forces 310
B.14 Criteria for the structure to support the external forces 312
B.15 Problems 314
References 316
Appendix C / Derivation of the strain energy theorems from the
virtual principles 317
C.1 Work and strain energy 317
C.2 Maximum and minimum strain energy and total potential energy 319
C.3 Theorem of minimum total potential energy 321
C.4 Theorem of minimum strain energy 322
C.5 Castigliano's theorem (Part J) 323
C.6 Hamilton's principle 323
C.7 Theorem of minimum total complementary potential theory 324
C.8 Theorem of minimum complementary strain energy 325
C.9 Castigliano's theorem (Part II) 326
C.10 Reissner's variational principle. 326
C.11 Comparison of the virtual principles and the strain energy theorems 327
References 328
Index 329
Contents
Volume 2: Design, Plates, Finite Elements
Preface
List of selected equations in Volume 1 referred to in Volume 2
Chapter 1 / Allowable stresses of Hight vehicle materials
1.1 Introduction
1.2 Tension, shear, and bearing allowable stresses
1.3 Temperature effects on allowable stresses
1.4 Allowable compression stresses
1.5 Allowable combined stresses
1.6 Creep effects on allowable stresses
1. 7 Room temperature fatigue effects upon allowable stresses
1.8 Temperature effects upon allowable fatigue stresses
1.9 Crack effects upon allowable fatigue stresses
1.10 Problems
References
Chapter 2 / Analysis and design of joints and splices
2.1 Introduction
2.2 Analysis of plate splices with axial tension forces
2.3 Multi-row tension splices
2.4 Joints with eccentric loading
2.5 Minimum weight design of splice for beam with rectangular cross section
2.6 Design of splices for I-beams and thin shear webs
2.7 Deflection effects on load distribution in splices
2.8 Temperature and inelastic effects on load distribution in splices
2.9 Welded joints
2.10 Bonded joints
2.11 Problems
References
ix
x Oontents of Volume 1!: Design, Plates, Finite Elements
Chapter 3 / Structural design of aircraft components
3.1 Introduction
3.2 Design of minimum weight columns without local buckling
3.3 Design of minimum weight sections with local buckling and crippling
3.4 Design of minimum weight columns with local buckling
3.5 Minimum weight design for stiffened panels in compression
3.6 Effective areas for stiffened panels
3.7 Effect of load intensity on wing design
3.8 Design of box beam cross sections with four spar caps
3.9 Analysis of diagonal tension beams
3.10 Problems
References
Chapter " / Analysis and design of pressurized structures
4.1 Introduction
4.2 Membrane stresses in thin shells
4.3 Cut-outs in thin shells with membrane stresses
4.4 Bending in circular cylindrical shells with axially symmetric loading
4.5 Bending in pressurized aircraft fuselages from stringers and frames
4.6 Bending of non-circular cross sections with internal pressure
4.7 Bending of non-circular fuselage rings with internal pressure
4.8 Bending of non-circular fuselage rings with point loads
4.9 Effect of internal pressure on buckling of cylindrical shells
4.10 Pressure stabilized structures
4.11 Problems
References
Chapter 5 / Approximate solutions using the virtual principles
5.1 Introduction
5.2 Approximate solutions for beams using the principle of virtual displacements
5.3 Approximate solutions for columns
5.4 The tapered cantilever beam with numerical integration
5.5 Tapered beam finite element matrices for columns
5.6 The unit load theorem and numerical integration
5.7 Approximate solutions for beams using the mixed virtual principle
5.8 Problems
References
Chapter 6 / Dynamics of simple beams
6.1 Introduction
6.2 Bending vibrations of simple beams
Oontents of Volume 1!: Design, Plates, Finite Elements
6.3 Forced motion of uniform beam
6.4 Approximate solutions for frequencies and mode shapes
6.5 Torsional vibrations of simple beams
6.6 Finite element matrices for beam frequencies
6.7 Flutter of wing segment with one degree of freedom
6.8 Flutter of wing segment with two degrees of freedom
6.9 Dynamic loads on beams
6.10 Problems
References
Chapter 1 / The plate equations
7.1 Introduction
7.2 The plate inplane case using the principle of virtual displacements
7.3 The plate inplane case using the principle of virtual forces
7.4 The plate inplane case using the mixed virtual principle
7.5 The plate bending case using the principle of virtual displacements
7.6 The plate bending case using the principle of virtual forces
7.7 The plate bending case using the mixed virtual principle
7.8 Combined inplane and lateral forces
7.9 Combined forces with large bending deflections
7.10 Buckling of plates
7.11 Plate vibrations
7.12 Problems
References
Xl
Chapter 8 / Approximate matrix equations for plate finite elements
8.1 Introduction
8.2 The point unknowns for the matrices
8.3 The methods to obtain the matrix equations
8.4 Inplane plate element matrices from the principle of virtual displacements
8.5 Inplane plate element matrices from the principle of virtual forces
8.6 Inplane plate element matrices from the mixed virtual principle
8.7 Bending plate element matrices from the principle of virtual displacements
8.8 Bending plate element matrices from the principle of virtual forces
8.9 Bending plate element matrices from the mixed virtual principle
8.10 Matrices for constant stress triangular elements
8.11 Problems
Chapter 9 / Matrix structural analysis using finite elements
9.1 Introduction
9.2 General beam elements in local coordinates
9.3 General beam elements in datum coordinat~es
9.4 Triangular plate elements with inplane forces
xii OontentlJ of Volume t: DelJign, Platu, Finite Elements
9.5 Assembly of finite elements by the virtual principles
References
Chapter 10 / Composite Materials
10.1 Introduction
10.2 Stress-strain equations for nonisotropic materials
10.3 Stress-strain equations for plane stress in an orthotropic material
10.4 Forces and moments in laminated plates
10.5 Stresses in laminated plates
10.6 Allowable stresses for laminated plates
10.7 Interlamina stresses
10.8 \ Joints in laminated plates
10.9 Bending deflections of laminated plates
10.10 Buckling loads for laminated plates
10.11 Vibrations of laminated plates
10.12 Problems
References
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