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 |  موضوع: كتاب Mechanics of Composite Materials الثلاثاء 01 سبتمبر 2020, 11:41 pm | |
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أخوانى فى الله
أحضرت لكم كتاب
Mechanics of Composite Materials
Second Edition
Robert M. Jones
Professor of Engineering Science and Mechanics
Virginia Polytechnic Institute and State University
Blacksburg, Virginia
و المحتوى كما يلي :
Contents
Preface to the Second Edition Xiii
Preface to the First Edition Xv
1 Introduction to Composite Materials . 1
1.1 Introduction . 1
1.2 the What - What is a Composite Material? . 2
1.2.1 Classification and Characteristics of Composite Materials 2
1.2.1.1 Fibrous Composite Materials 3
1.2.1.2 Laminated Composite Materials 6
1.2.1.3 Particulate Composite Materials 8
1.2.1.4 Combinations of Composite Materials 10
1.2.2 Mechanical Behavior of Composite Materials 11
1.2.3 Basic Terminology of
Laminated Fiber - Reinforced Composite Materials 15
1.2.3.1 Laminae 15
1.2.3.2 Laminates 17
1.2.4 Manufacture of
Laminated Fiber - Reinforced Composite Materials 18
1.2.4.1 Initial Form of Constituent Materials 18
1.2.4.2 Layup 19
1.2.4.3 Curing 23
1.3 the Why - Current and Potential Advantages
Of Fiber - Reinforced Composite Materials . 26
1.3.1 Strength and Stiffness Advantages 27
1.3.2 Cost Advantages 31
1.3.3 Weight Advantages 36
1.4 the How - Applications of Composite Materials . 37
1.4.1 Introduction 37
1.4.2 Military Aircraft 38
1.4.2.1 General Dynamics F - 111 Wing - Pivot Fitting 38
1.4.2.2 Vought a - 7 Speedbrake 40
1.4.2.3 Vought S - 3a Spoiler 42
1.4.2.4 Boeing F - 18 43
1.4.2.5 Boeing Av - Bb Harrier 44
1.4.2.6 Grumman X - 29a 45
1.4.2.7 Northrop Grumman B - 2 45
1.4.2.8 Lockheed Martin F - 22 46
1.4.3 Civil Aircraft 47
1.4.3.1 Lockheed L - 1011 Vertical Fin 47
1.4.3.2 Rutan Voyager 48
1.4.3.3 Boeing 777 49
1.4.3.4 High - Speed Civil Transport 49
1.4.4 Space Applications 50
1.4.5 Automotive Applications 50
Vvi Content}
1.4.6 Commercial Applications 52
1.5 Summary 52
Problem Set 1 53
References 53
2 Macromechanical Behavior of a Lamina 55
2.1 Introduction . 55
2.2 Stress - Strain Relations for Anisotropic Materials 56
2.3 Stiffnesses, Compliances, and
Engineering Constants for Orthotropic Materials . 63
2.4 Restrictions on Engineering Constants . 67
2.4.1 Isotropic Materials 67
2.4.2 Orthotropic Materials 68
Problem Set 2.4 70
2.5 Stress - Strain Relations for Plane Stress
In an Orthotropic Material . 70
2.6 Stress - Strain Relations for
A Lamina of Arbitrary Orientation 74
Problem Set 2.6 84
2.7 Invariant Properties of an Orthotropic Lamina . 85
Problem Set 2.7 87
2.8 Strengths of an Orthotropic Lamina . 88
2.8.1 Strength Concepts 88
2.8.2 Experimental Determination of Strength and Stiffness 91
2.8.3 Summary of Mechanical Properties 100
Problem Set 2.8 102
2.9 Biaxial Strength Criteria for an Orthotropic Lamina 102
2.9.1 Maximum Stress Failure Criterion 106
2.9.2 Maximum Strain Failure Criterion 107
2.9.3 Tsai - Hill Failure Criterion 109
2.9.4 Hoffman Failure Criterion 112
2.9.5 Tsai - Wu Tensor Failure Criterion 114
2.9.6 Summary of Failure Criteria 118
Problem Set 2.9 118
2.10 Summary .• • . 118
References 119
3 Micromechanical Behavior of a Lamina 121
3.1 Introduction . 121
3.2 Mechanics of Materials Approach to Stiffness . 126
3.2.1 Determination of E1 127
3.2.2 Determination of E2 129
3.2.3 Determination of V12 132
3.2.4 Determination of G12 133
3.2.5 Summary Remarks 135
Contents Vii
Problem Set 3.2 135
3.3 Elasticity Approach to Stiffness 137
3.3.1 Introduction 137
3.3.2 Bounding Techniques of Elasticity 137
3.3.3 Exact Solutions 145
3.3.4 Elasticity Solutions With Contiguity 147
3.3.5 the Halpin - Tsai Equations 151
3.3.6 Summary Remarks 157
Problem Set 3.3 158
3.4 Comparison of Approaches to Stiffness 158
3.4.1 Particulate Composite Materials 158
3.4.2 Fiber - Reinforced Composite Materials 160
3.4.3 Summary Remarks 163
3.5 Mechanics of Materials Approach to Strength . 163
3.5.1 Introduction 163
3.5.2 Tensile Strength in the Fiber Direction 164
3.5.3 Compressive Strength in the Fiber Direction 171
Problem Set 3.5 184
3.6 Summary Remarks on Micromechanics . 184
References 185
4 Macromechanical Behavior of a Laminate 187
4.1 Introduction . 187
Problem Set 4.1 190
4.2 Classical Lamination Theory 190
4.2.1 Lamina Stress - Strain Behavior 191
4.2.2 Stress and Strain Variation in a Laminate 191
4.2.3 Resultant Laminate Forces and Moments 195
4.2.4 Summary 199
Problem Set 4.2 202
4.3 Special Cases of Laminate Stiffnesses . 203
4.3.1 Single~layered Configurations 203
4.3.2 Symmetric Laminates 206
4.3.3 Antisymmetric Laminates 214
4.3.4 Unsymmetric Laminates 218
4.3.5 Common Laminate Definitions 219
4.3.6 Summary Remarks 221
Problem Set 4.3 222
4.4 Theoretical Versus Measured Laminate Stiffnesses 222
4.4.1 Inversion of Stiffness Equations 222
4.4.2 Special Cross - Ply Laminate Stiffnesses 224
4.4.3 Theoretical and Measured Cross - Ply Laminate Stiffnesses 229
4.4.4 Special Angle - Ply Laminate Stiffnesses 232
4.4.5 Theoretical and Measured Angle - Ply Laminate Stiffnesses 235
4.4.6 Summary Remarks 237
Problem Set 4.4 237
4.5 Strength of Laminates 237
4.5.1 Introduction 237(
Viii Contents
4.5.2 Laminate Strength - Analysis Procedure 240
4.5.3 Thermal and Mechanical Stress Analysis 242
4.5.4 Hygroscopic Stress Analysis 245
4.5.5 Strength of Cross - Ply Laminates 246
4.5.6 Strength of Angle - Ply Laminates 255
4.5.7 Summary Remarks 258
Problem Set 4.5 260
4.6 Interlaminar Stresses . 260
4.6.1 Classical Lamination Theory 262
4.6.2 Elasticity Formulation 264
4.6.3 Elasticity Solution Results 267
4.6.4 Experimental Confirmation of Lnterlaminar Stresses 269
4.6.5 Lnterlaminar Stresses in Cross - Ply Laminates 271
4.6.6 Implications of Lnterlaminar Stresses 272
4.6.7 Free - Edge Delamination - Suppression Concepts 274
Problem Set 4.6 275
References 275
5 Bending, Buckling, and Vibration of Laminated Plates • .• 277
5.1 Introduction . 277
5.2 Governing Equations for Be~, Buckling, and
Vibration of Laminated Plates . 279
5.2.1 Basic Restrictions, Assumptions, and Consequences 279
5.2.2 Equilibrium Equations for Laminated Plates 282
5.2.3 Buckling Equations for Laminated Plates 285
5.2.4 Vibration Equations for Laminated Plates 288
5.2.5 Solution Techniques 288
5.3 Deflection of Simply Supported Laminated Plates
Under Distributed Transverse Load . 289
5.3.1 Specially Orthotropic Laminated Plates 290
5.3.2 Symmetric Angle - Ply Laminated Plates 291
5.3.3 Antisymmetric Cross - Ply Laminated Plates 295
5.3.4 Antisymmetric Angle - Ply Laminated Plates 298
Problem Set 5.3 301 -
5.4 Buckling of Simply Supported Laminated Plates
Under in - Plane Load 301
5.4.1 Specially Orthotropic Laminated Plates 303
5.4.2 Symmetric Angle - Ply Laminated Plates 306
5.4.3 Antisymmetric Cross - Ply Laminated Plates 307
5.4.4 Antisymmetric Angle - Ply Laminated Plates 312
Problem Set 5.4 315
5.5 Vibration of Simply Supported Laminated Plates ••.••••• ·315
5.5.1 Specially Orthotropic Laminated Plates 315
5.5.2 Symmetric Angle - Ply Laminated Plates 317
5.5.3 Antisymmetric Cross - Ply Laminated Plates 318
5.5.4 Antisymmetric Angle - Ply Laminated Plates 320
Problem Set 5.5 322
5.6 Summary Remarks on Effects of Stiffnesses 323
References 329
(
Contents Ix
6 Other Analysis and Behavior Topics 331
6.1 Introduction . 331
6.2 Review of Chapters 1 Through 5 • .•• .• • 332
6.3 Fatigue .• •• ••• •.• .• .• . 333
6.4 Holes in Laminates .••• .• • 336
6.5 Fracture Mechanics .• • .• .• .• • • • 339
6.5.1 Basic Principles of Fracture Mechanics 340
6.5.2 Application of Fracture Mechanics to Composite Materials 343
6.6 Transverse Shear Effects •• .•• .• .•• .• 345
6.6.1 Exact Solutions for Cylindrical Bending 346
6.6.2 Approximate Treatment of Transverse Shear Effects 350
6.7 Postcuring Shapes of Unsymmetric Laminates 356
6.8 Environmental Effects . 359
6.9 Shells • •• .•.• •• .• • .• .• 361
6.10 Miscellaneous Topics . 362
References 362
7 Introduction to Design of Composite Structures 367
7.1 Introduction.• ••.•••••.• • •• • • .• • • 368
7.1.1 Objectives 368
7.1.2 Introduction to Structural Design 368
7.1.3 New Uses of Composite Materials 368
7.1.4 Manufacturing Processes 368
7.1.5 Material Selection 369
7.1.6 Configuration Selection 369
7.1.7 Joints· 369
7.1 .8 Design Requirements 370
7.1.9 Optimization 370
7.1.1 O Design Philosophy 371
7.1.11 Summary 372
7.2 Introduction to Structural Design 372
7.2.1 Introduction 372
7.2.2 What is Design? 372
7.2.3 Elements of Design 376
7.2.4 Steps in the Structural Design Process 380
7.2.4.1 Structural Analysis 381
7.2.4.2 Elements of Analysis in Design 381
7.2.4.3 Failure Analysis 382
7.2.4.4 Structural Reconfiguration 383
7.2.4.5 Iterative Nature of Structural Design 384
7.2.5 Design Objectives and Design Drivers 385
7.2.6 Design - Analysis Stages 386
7.2.6.1 Preliminary Design - Analysis 387
7.2.6.2 Intermediate Design - Analysis 388
7.2.6.3 Final Design - Analysis 388
7.2.7 Summary 389x Contents
(
7.3 Materials Selection 389
7.3.1 Introduction 389
7.3.2 Materials Selection Factors 390
7.3.3 Fiber Selection Factors 391
7.3.4 Matrix Selection Factors 392
7.3.5 Importance of Constituents 393
7.3.6 Space Truss Material Selection Example 394
7.3.7 Summary 400
7.4 Configuration Selection 400
7.4.1 Introduction 400
7.4.2 Stiffened Structures 400
7.4.2.1 Advantages of Composite Materials in
Stiffened Structures 401
7.4.2.2 Types of Stiffeners 403
7.4.2.3 Open - Versus Closed - Section Stiffeners 405
7.4.2.4 Stiffener Design 407
7.4.2.5 Orthogrid 410
7.4.3 Configuration in Design Cost 411
7.4.4 Configuration Versus Structure Size 413
7.4.5 Reconfiguration of Composite Structures 414
7.4.6 Summary 417
7.5 Laminate Joints .: - : - ,_ . 417
7.5.1 Introduction 417
7.5.2 Bonded Joints 419
7.5.3 Bolted Joints 420
7.5.4 Bonded - Bolted Joints 421
7.5.5 Summary 422
7.6 Design Requirements and Design Failure Criteria . 422
7.6.1 Introduction 422
7.6.2 Design Requirements 422
7.6.3 Design Load Definitions 424
7.6.4 Summary 425
7.7 Optimization Concepts . 425
7.7.1 Introduction 425
7.7.2 Fundamentals of Optimization 426
7.7.2.1 Structural Optimization 426
7.7.2.2 Mathematics of Optimization 429
7.7.2.3 Optimization of a Composite Laminate 431
7.7.2.4 Strength Optimization Programs 435
7.7.3 Invariant Laminate Stiffness Concepts 440
7.7.3.1 Invariant Laminate Stiffnesses 440
7.7.3.2 Special Results for Invariant Laminate Stiffnesses 443
7.7.3.3 Use of Invariant Laminate Stiffnesses in Design 446
Problem Set 7.7.3 447
7.7.4 Design of Laminates 447
7.7.5 Summary 453
7.8 Design Analysis Philosophy for
Composite Structures .• . 453
7.8.1 Introduction 453
7.8.2 Problem Areas 454
7.8.3 Design Philosophy 455
7.8.4 'anisotropic' Analysis 455
7.8.5 Bending - Extension Coupling 456
7.8.6 Micromechanics 457
7.8.7 Nonlinear Behavior 458
7.8.8 Lnterlaminar Stresses 459
7.8.9 Transverse Shearing Effects 460
7.8.10 Laminate Optimization 461
7.8.11 Summary 462
Contents Xi
7.9 Summary .• 463
References 465
Appendix a: Matrices and Tensors 467
A.1 Matrix Algebra 467
A.1.1 Matrix Definitions 467
A.1.2 Matrix Operations 470
A.2 Tensors .• . 472
A.2.1 Transformation of Coordinates 473
A.2.2 Definition of Various Tensor Orders 474
A.2.3 Contracted Notation 475
A.2.4 Matrix Form of Tensor Transformations 476
Reference 477
Appendix B: Maxima and Minima of
Functions of a Single Variable • 479
Reference 483
Appendix C: Typical Stress - Strain Curves 485
C.1 Fiberglass - Epoxy Stress - Strain Curves • 485
C.2 Boron - Epoxy Stress - Strain Curves . 485
C.3 Graphite - Epoxy Stress - Strain Curves ••• • • . 485
References 494
Appendix D: Governing Equations for Beam Equilibrium and
Plate Equilibrium, Buckling, and Vibration . 495
D.1 Introduction . 495
D.2 Derivation of Beam Equilibrium Equations • .• 495
D.3 Derivation of Plate Equilibrium Equations . 498
D.4 Plate Buckling Equations 505
D.5 Plate Vibration Equations •.• •.• • • . 506
References 506
Index . 507index
- Aadams, D. F. 146, 152, 156, 254, 362
Adelman, H. M. 117
Almroth, B. 0. 284, 506
Alva, F. 48
Ambartsumyan, S. A. 91, 350, 355, 361
Analysis 372 - 373, 376
Analysis in Design 381
Angle - Ply Laminate 216 - 217
Antisymmetric 216 - 217, 222, 233,
298 - 301, 312 - 315, 320 - 322
Bending 291 - 295, 298 - 301
Buckling 306 - 307, 312 - 315, 328
Interlaminar Stresses 260 - 275
Stiffnesses 232 - 237
Strength 255 - 258
Symmetric 212 - 213, 233, 291 - 295,
306 - 307, 317 - 318
Vibration 317 - 318, 320 - 322
Anisotropic Lamina 77 - 79
Anisotropic Material
See Also Anisotropy
Anisotropic Behavior 14, 80
Definition of 12
Engineering Constants 78 - 79
Invariant Properties of 85 - 87
Plane Stress State 70
Strain - Stress Relations 60, 79
Stress - Strain Relations 56, 79
Anisotropy 336 - 337, 343, 454 - 456
Antisymmetric Laminate 214 - 222
Angle - Ply 216 - 217, 222, 233,
298 - 301, 312 - 315, 320 - 322
Bending 295 - 301
Buckling 307 - 315
Cross - Ply 215 - 216, 226, 295 - 298,
307 - 312, 318 - 320
Vibration 318 - 322
Applications of Composite Materials
Automotive 50 - 52
Civil Aircraft 4 7 - 50
Commercial 52
Military Aircraft 38 - 46
Space 50
(
Inaex 507
Ashton, J. E. 199, 289, 292 - 295,
306 - 307, 328 - 329, 350, 355, 360, 364,
435,454,456,485, 489 - 494
Asymmetric Laminate
See Unsymmetric Laminate
Axial Stiffness 91 - 95, 101, 127 - 128, 149
Axial Strength 88, 91, 93, 101
- Bbaker, D. J. 272
Batdorf Shell Curve Parameter 361
Beam Boundary Conditions 496 - 498
Beam Equilibrium Equations 495 - 498
Beer, R. 350
Bend - Twist Coupling 198 - 199, 211 - 215,
233, 235, 278 - 279, 290 - 295, 306 - 307,
317 - 318, 323, 327 - 328, 439, 454 - 455
Bending of Laminated Plates 277 - 278,
282 - 285, 289 - 301, 323,360
Antisymmetric Angle - Ply
Laminates 298 - 301
Antisymmetric Cross - Ply
Laminates 295 - 298
Boundary Conditions 283 - 285
Cylindrical Bending 346 - 350
Equilibrium Equations 282 - 285
Solution Techniques 288 - 289
Specially Orthotropic
Laminates 290 - 291
Symmetric Angle - Ply
Laminates 291 - 295
Unsymmetric Cross - Ply
Laminates 324 - 325
Bending - Extension Coupling 7, 198 - 199,
206, 214 - 222, 227 - 228, 277 - 279, 290,
295 - 301, 307 - 315, 317 - 327, 355, 361,
408, 439, 454, 456 - 457
Benign Failure 382
Berg, K. R. 419
Bernoulli 374, 399
Bert, C. W. 91
Betti's Law 66
Biaxial Strength Criteria508 Mecha!.~ - of Composite Materials
For a Lamina 102 - 118
Hoffman Failure Criterion 105,
112 - 114, 422
Maximum Strain Failure Criterion 105,
107 - 109
Maximum Stress Failure Criterion 105,
106 - 107
Tsai - Hill Failure Criterion 105,
109 - 112, 115 - 116, 241,246,
249 - 250, 256 - 258
Tsai - Wu Tensor Failure Criterion 105,
114 - 118
Bifurcation 302
Bimetallic Strip 6 - 7, 202
Bimetals 6 - 7
Boeing Av - Bb Harrier 44 - 45
Boeing F - 18 43 - 44
Boeing 777 49
Boron Fibers 4
Boron - Aluminum 392, 458
Boron - Epoxy 17, 19, 21 - 22, 30, 67, 69,
81 - 82, 91, 100 - 101, 113 - 118, 147,
152 - 155, 182, 221, 298, 304, 306,
311 - 312, 316,334, 336 - 337, 359,380,
392,421,457, 485,489 - 491
Boundary Conditions
Beam 496 - 498
Plate 283 - 285, 287 - 288, 501 - 503
Boundary Layer Effect 267
Broutman, L. J. 363
Browning, C. E. 246, 360
Brozovic, G. 48
Brush, D. 0. 506
Buckling 277, 285 - 288, 301 - 315, 323,
357, 360 - 361, 374, 381 - 382, 398, 427
Buckling of Laminated Plates 277 - 278,
285 - 288, 301 - 315, 323 - 329
Antisymmetric Angle - Ply
Laminates 312 - 315
Antisymmetric Cross - Ply
Laminates 307 - 312
Boundary Conditions 287 - 288
Governing Equations 285 - 288
Initial Imperfections 303
Solution Techniques 288 - 289
Specially Orthotropic
Laminates 303 - 305
Symmetric Angle - Ply
Laminates 306 - 307
Unsymmetric Cross - Ply
Laminates 326 - 327
Bulk Modulus 67
- Ccarbon Fibers 4
Carbon Matrix Materials 23, 392
Carbon - Carbon 362
Card, M. F. 221, 406, 408
Caril, B. 48
Catastrophic Failure 382
Ceramic Matrix Materials 23, 392
Chamis, C. C. 120, 137, 147, 158, 306,
345
Cheng, S. 361
Chentsov Coefficients 80, 84
Chen, E. P. 345
Charon, T. 363 - 364
Chou,p.c. 89,362
Chou, T. W. 245 - 246
Clad Metals 7
Classical Lamination Theory 190 - 203,
260 - 264, 267, 271 - 272, 274, 337,
346 - 348, 350 - 352, 354, 356
Bending - Extension Coupling 198 - 199
Cylindrical Bending 346 - 350
Laminate Forces and
Moments 195 - 199
Middle - Surface Curvatures 194
Middle - Surface Strains 194
Strain and Stress Variation 191 - 195
Cocuring 25
Coefficients of Moisture Diffusion 245
Coefficients of Moisture Expansion 245
Coefficients of Mutual Influence 79, 84
Coefficients of Thennal Expansion 242,
245
Cole, B. W. 113 - 114, 116 - 117
Compliance Matrix
See Compliances
Compliances
Elastic Constants 58
For Anisotropic Material 79
For Orthotropic Material 64 - 66
In Stress - Strain Relations 58, 118
Mnemonic Notation 58
Relation to Stiffnesses for Orthotropic
Materials 66
Restrictions on 68
Symmetry of 58
Composite Materials
Advantages of 2
Characteristics of 2 - 11
Classification of 2 - 11
Definition of 2
History of 2
Manufacturing of 18 - 26
Mechanical Behavior of 11 - 14
Tailoring of 12, 18
Composite Structures Cost 368 - 369, 375,
412,425
Composite Structures Weight 375, 377,
425,427
Concentric Cylinder Model 144, 147
Concentric Spheres Model 143
Configuration Selection 369, 376,
400 - 417
Constitutive Relations
See Strain - Stress Relations
See Stress - Strain Relations
Contiguity 147 - 151
Contiguity Factor 149 - 151, 160 - 163
Degree of 147
Contracted Notation 56, 475
Strains 56, 475
Stresses 56,115,475
Corten, H. T. 120,345,363
Cost 31 - 36, 47 - 48, 411,424, 463 - 464
See Also Composite Structures Cost
See Also Life - Cycle Cost
Coupling 7,211,215
See Also Eccentrically Stiffened Plates
And Shells
Bend - Twist 198 - 199, 211 - 215, 233,
235, 278 - 279, 290 - 295, 306 - 307,
317 - 318, 323, 327 - 328, 439,
454 - 455
Bending - Extension 7, 198 - 199, 206,
214 - 222, 227 - 228, 277 - 279, 290,
295 - 301, 307 - 315, 317 - 327, 355,
361,408,439, 454,456 - 457
Shear - Extension 14, 59, 77, 81, 91,
97,205, 211 - 213, 230, 235 - 237, 258,
269, 273, 277 - 278, 291, 306, 317,
348, 439, 454 - 455
Shear - Shear 80
Stiffnesses 198, 277
!henna! 252 - 253, 258
Crack Propagation 334, 339 - 345
Cracks 333 - 334, 339 - 345, 359
Cramer's Rule 472
Crocker, J. F. 47
Cross - Beam Test 99 - 100
Cross - Ply Laminate 188, 206, 210, 213,
215 - 216, 224 - 232, 354
Antisymmetric 215 - 216, 226,
295 - 298, 307 - 312, 318 - 320
Bending 290 - 291, 295 - 298, 324 - 326
Buckling 303 - 305, 307 - 312, 326 - 327
Inter1aminar Stresses 271, 273
Stiffnesses 224 - 232
Strength 246 - 255
Symmetric 210 - 211, 225, 354
Unsymmetric 323 - 327
Vibration 315 - 320, 327 - 328
Cross - Ply Ratio 224
Cruse, T. A. 345
Curing 23 - 26
Cylindrical Bending 346 - 350
- Ddamage
Fatigue 333 - 336
Growth 333 - 336
Mechanics 333
Daniel, I. M. 269 - 270
Davies, G. J. 165, 167
Davis, J. G. 364
Index
De Malherbe, M. C. 152, 156
Debonding 261
See Also Delamination
Deflection 382
Deflection of Plates
See Bending of Laminated Plates
Delamination 260, 271 - 272, 333
Delamination - Suppression
Concepts 274 - 275
Design 373, 431
Buckling - Critical 399
Constraints 434
Cost - Effective 398
Isotropic Plate 431
509
Laminate 431 - 440, 446 - 453, 461 - 462
Least - Weight 398
Merit Function 434
Simplified Design Space 439
Stiffness - Critical 399
Strength - Critical 399
Testing During 388, 389
Design Drivers 372, 378, 382, 385 - 386,
390,463
Design Elements 376 - 380
Design Failure Criteria 370, 422 - 425
Design Load Definitions 424 - 425
Design Load Limit 424
Design Ultimate Load 424
Ultimate Load 424
Design Modification
See Design Reconfiguration
Design Objectives 372, 385, 448
Design Parameters
See Design Variables
Design Philosophy 371,374
Design Requirements 370, 373, 380 - 381,
384,389, 422 - 425,427
Design Space 377
Design Variables 370 - 371, 373, 377 - 378,
383,426
Design - Analysis 386
Final 387 - 389
Intennediate 387 - 388
Iterations 384 - 385
Philosophy 453 - 463
Preliminary 387 - 388
Stages 386 - 389
Design - Analysis Iterations 384 - 385
Design - Analysis Philosophy 453 - 463
Design - Analysis Stages 386 - 389
Detailed Design 388510 Mej
,s of Composite Materials
Deterministic 373 - 374, 381, 432, 434
Dickerson, E. O. 69
Dietz, a. G. H. .3
Diffusion Coefficient 245
Dimartino, B. 69
Dispersion - Stiffened Composite
Material 135, 137 - 143, 158 - 159
Doner, D. A. 152,156,254
Dong, S. B. 191, 361
Dow, N. F. 169 - 172, 1n, 181 - 182
Duke, J. C. 333
- Eeccentrically Stiffened Plates and
Shells 221
See Also Coupling
Eisenmann, J. A. 335, 345
Ekvall, J.c. 47, 135
Elastic Constants
See Also Compliances, Engineering
Constants, Stiffnesses
Definition 118
Restrictions on 67
Elasticity 264 - 268, 340 - 341, 343,
346 - 348, 350, 353 - 354
Elasticity Approach to
Micromechanics 122, 126, 137 - 163
Bounding Techniques 137 - 144
Contiguity 147 - 151
Discrete Element Approaches 125,
137,145
Exact Solutions 137, 145 - 147
Halpin - Tsai Equations 151 - 158
Microstructure Theories 137, 158
Self - Consistent Models 137, 147
Statistical Approaches 137
Variational Techniques 137
Electrical Conductivity 359
Energy 424
Engineering Constants 63 - 64, 118, 191
Apparent for Orthotropic Lamina 80
Restrictions on 67
Environmental Effects 359 - 361
Epoxy 5, 393 - 394
Eudaily, a. R. 47 - 48
Euler 374, 399
Ewing, M. S. 329
Expansional Strains 242 - 246, 360
Extrema of Material Properties 81 - 85
118 '
- Ffactor of Safety 382 - 383, 448
Failure 370
Benign 382
Catastrophic 382
Modes 381
Failure Analysis 382 - 383
Failure Criteria 370
For a Lamina 102 - 118
For a Laminate 237 - 260
Hoff:nan Criterion 105, 112 - 114, 422
Maximum Strain Criterion 105
10? - 109, 112, 435, 453 '
Maximum Stress Criterion 105 - 107
112 '
Tsai - Hill Criterion 105, 109 - 112,
115 - 116, 241, 246, 249 - 250
256 - 258 '
. Tsai - Wu Criterion 105, 114 - 118
Failure Envelopes 102 - 105
Fatigue 2, 7, 272, 333 - 336 339 370
398,440 ' ' '
Fatigue Life 390
Fatigue Strength 272, 333 - 336, 339
Fem, P. 363
Fiber Buckling 171 - 183
Extensional Mode 171 - 178, 180 - 183
Shear Mode 171 - 174, 179 - 183
Transverse Mode 171 - 178 180 - 1b3
Fiber Misalignment Factor 149' 160
Fiber Selection Factors 391 '
Fiber - Matrix Interface 339 360
Fib~r - Reinforced Laminated ~omposite Matenals
Advantages of 11
Applications of 37 - 52
Constituents of 15 - 18
Curing of 23 - 26
Current and Potential Uses of 37_38
Definition of 11
Lay - Up of 19 - 23
Manufacturing of 18 - 26
Molding of 20 - 23
Quality Control Factors 26
Tailoring of 12 18
Fiber - Volume Fracti~n 123
Fiberglass - Epoxy 1o
Fibers
Boron 4
Carbon 4
Contiguity Factor 147, 149 - 151,
160 - 163
Definition of 3
Diamond Array 145 - 146
Function of 15
Glass 3
Graphite 4
Hexagonal Array 146
Initial Form 18
Misalignment Factor 149, 160
Properties of 3 - 4, 16
Random Arrangement 147
Restrictions on Micromechanical Behavior 124
Square Array 146
Staggered Square Array 145 - 146
Fibrous Composite Materials
Definition of 2
Filament Winding 19 - 20, 74,119,410
Final Design - Analysis 388 - 389
Finite Difference Approach 145, 266 - 267,
289
Finite Element Approach 125, 145, 289
First - Ply Failure Load 452
Flaws 339, 343
Flom, D. G. 4
Fourier Series 289, 291 - 292, 296,328
Foye, R. L. 152, 154, 272
Fracture Mechanics 339 - 345
Application to Composite
Materials 343 - 345
Basic Principles of 340 - 342
Crack Extension Modes 340
Fracture Process 339
Strain - Energy - Release Rate 340 - 341
Stress - Intensity Factors 342 - 344
Free Thermal Strain 242
Fried, N. 359
- Ggalerkin Method 289, 306
Galvanic Corrosion 361
General Dynamics F - 111 Wing - Pivot
Fitting 38 - 40
Generally Orthotropic Lamina 77 - 79
See Also Orthotropic Lamina
Generally Orthotropic Laminate 214
Gere, J.m. 174 - 175, 301, 506
Girkmann, K. 350
Glass Fibers 3
Glass - Epoxy 22, 30 - 31, 74, 81 - 82, 91,
100 - 101, 105 - 107, 109, 111 - 113, 118,
143, 149, 152 - 155, 160, 162, 164,
171 - 172, 180 - 182, 334,336,343, 359,
361, 380, 485 - 488
Glass - Transition Temperature 360
Goland, M. 419
Graphite Fibers 4
Graphite - Epoxy 17, 29 - 30, 33, 35, 38, 41,
43 - 44, 47 - 48, 50, 52, 84, 98, 100 - 101,
113 - 114, 147, 152, 184, 221, 245, 267,
269, 297 - 298, 300, 310 - 313, 319,321,
325 - 328, 336, 347, 354 - 361, 369, 380,
391 - 392, 395 - 397, 415, 421, 457 - 458,
485, 491 - 494
Greszczuk, L.b. 171, 182, 336 - 338
Griffith, a. A. 340
Grumman X - 29a 45
Gurland, J. 158
- Hhadcock, a. N. 439
Hahn,h.t. 99,362
Halpin - Tsai Equations 123, 126, 137,
151 - 157
511
Halpin, J.c. 97 - 98, 119 - 120, 123, 126,
151 - 155, 199,363,365,466,485,
489 - 494
Hansen, M. P. 345
Han, B. 269
Hart - Smith, L. J. 103, 420, 422
Hashin, 2. 143 - 144, 147, 159, 163, 170,
362
Hatfield, S. J. 348
Henkel, J. 48
Henneke, E. G. 333
Hennemann,j.c.f. 286
Herakovich, C. T. 362
Hermans, J. J. 147, 151 - 152
Herrmann, L. A. 145
Heterogeneity 11, 122
Hewitt, R. L. 152, 156
High - Speed Civil Transport 49 - 50
Hill, a. 105, 109, 111 - 112, 115 - 116, 147,
151,241,246,249,256,258,422
Hinger, R. J. 329
Hoffman Failure Criterion 105, 112 - 114,
422
Hoffman, O. 112,422
Holes in Laminates 336 - 339
Hollister, G. S. 362
Homogeneity 11, 122
Hooke's Law 118
Howell, H. B. 100
Ho, P. B. C. 361
Humidity 359
Husman, G. E. 246, 360
Hyer, M. W. 356 - 359
Hygroscopic Stresses 245 - 246
- 1 -
Lfju, P. 269
Impact Resistance 345
Inhomogeneity 11 - 12
Definition of 11
Innovative Fabrication 463 - 464
Interaction Strength 114 - 118
Lnterlaminar Stresses 260 - 275, 459 - 460
Angle - Ply Laminates 260 - 275512 Mechanics of Composite Materials
Boundary Layer Effect 267
Cross - Ply Laminates 271, 273
Delamination - Suppression
Concepts 274 - 275
Elasticity Solution 264 - 268
Experimental Confirmation 269 - 270
Implications 272 - 274
Intermediate Design - Analysis 388
Invariant Properties 85 - 87
Invariant Stiffness Concepts 85 - 87,
440 - 447
Irwin, G. R. 340 - 341
Isotropic Material
See Also Isotropy
Definition of 11
Isotropic Behavior 12 - 14
Plane Stress State 70
Strain - Stress Relations 62
Stress - Strain Relations 60
Iteration 373, 380, 384, 424
- Jjackson, a. C. 47 - 48
Johnson, R. 48
Joints 369, 376 - 377, 383, 417 - 422
Bolted 417, 420 - 421
Bonded 417 - 420
Bonded - Bolted 417, 421
Failures in Bolted Joints 420 - 421
Failures in Bonded Joints 420
Shimmed 421
Jones, R. M. 81, 91, 99, 221, 275, 286,
307 - 308, 310 - 312, 314, 320, 322 - 327,
361 - 362, 364,406,408,457,506
Judge, J. F. 26
June, R. R. 182 - 183
- Kkaminski, B. E. 335, 345
Keiffer, R. 158
Kelly, a. 165, 167
Kevlar 49@ - Epoxy 100 - 101
Kevlar - Epoxy 30, 413, 457 - 458
Kim, R. Y. 113 - 114
Kirchhoff Free - Edge Condition 283, 352
Kirchhoff Hypothesis 192 - 195, 281,
347 - 348, 504
Kirchhoff Shear Force 502
Kirchhoff - Love Hypothesis 192 - 195
Konish, H.j., Jr. 345
Krock, R. H. 363
- Llager, J. R. 182 - 183
Lamina
Definition of 15, 55
Design 85
Invariant Properties of 85 - 87
Restrictions on Micromechanical Behavior 124
Strength 88 - 118
Stress - Strain Behavior 191
Unidirectionally Reinforced 15, 27 - 28
Lamina Stiffness
In Fiber Direction 88, 91, 93 - 95
Shear 88,91,96 - 101,115
Transverse to Fiber Direction 88, 91,
95 - 96
Lamina Strength
In Fiber Direction 88, 91, 93 - 95
Shear 88, 91, 96 - 101, 115
Transverse to Fiber Direction 88, 91,
95 - 96
Laminate 435
See Also Angle - Ply Laminate
See Also Cross - Ply Laminate
Antisymmetric 214 - 222
Balanced 220 - 221
Curing 206,239
Cylindrical Bending 346 - 350
Definition of 6, 17, 187
Design 431 - 440, 446 - 453, 461 - 462
Displacements 192 - 193
Environmental Effects 359 - 361
Forces and Moments 195 - 199
Fracture Mechanics 339 - 345
Holes in 336 - 339
Hybrid 221
Interlaminar Stresses 260 - 275
Invariant Stiffness Concepts 440 - 447
Joints 417 - 422
Macromechanical Behavior
Of 187 - 275
Manufacturing 18 - 26
Notation 219
Postcuring Shapes 356 - 359
Purpose of 18
Quasi - Isotropic 219 - 220, 435, 445
Regular 210 - 212, 216 - 217, 219
Stacking Sequence 219, 240, 272,
379,449
Stiffnesses 198 - 237
Strain and Stress Variation 191 - 195
Strength 237 - 260
Analogy to Plate Buckling 237
Analysis Procedure 240 - 242
Fatigue 272, 333 - 336, 339
Symmetric 206 - 214, 354
Symmetry 439
Tailoring 378
Temperature - Dependent Properties
Of 197
Unsymmetric 206,214, 218 - 219,
356 - 359
Laminate Behavior
Brittle 449
Ductile 449
Energy Absorption 449
Fatigue 449
Load - Deflection Behavior 449
Laminate Design 431 - 440, 446 - 453,
461 - 462
Laminae Reorientation 436
Laminate Design Problem 434, 450
Laminate Life - Prediction Techniques 451
Laminate Optimization 431 - 440, 446 - 453,
461 - 462
Laminate Stacking Sequence 379, 449
Laminate Strength Analysis
Procedure 450
Laminate Tailoring 378
Laminated Composite Materials
See Also Laminate
Definition of 2, 6
Types of 6 - 8
Laminated Glass 7 - 8
Laminated Plates 277 - 329
Behavioral Restrictions and Assumptions 279 - 282
Bending 277 - 279, 282 - 285, 289 - 301,
323 - 325
Boundary Conditions 283 - 285,
287 - 288
Buckling 277 - 279, 285 - 288, 301 - 315,
323 - 329
Governing Equations 279 - 289
Initial Imperfections 303
Kirchhoff Hypothesis 281
Stiffnesses 325 - 326
Vibration 277 - 279, 288, 315 - 322, 327
Laminated Shells 361
Langhaar, H. L. 292, 483
Latour, R. A. 183
Law of Mixtures
See Rule of Mixtures
Least - Cost Structures 368 - 369, 375,412,
425
Least - Weight Structures 375,377,425,
427
Leissa, a. W. 295,298,329
Lekhnitskii, S. G. 79, 336
Lempriere, B. M. 68
Liebowitz, H. 364, 466
Life 424
Life - Cycle Cost 32, 368, 385
Lightning 359
Linear Stress - Strain Behavior 16 - 17,
91 - 99, 102
Lockheed L - 1011 Vertical Fin 47 - 48
Lockheed Martin F - 22 46
Longitudinal Stiffness 101, 127 - 128, 149
Index 513
Longitudinal Strength 88, 91 - 95, 101
Lubin, G. 394
- Mmacdonald, D. 118
Macromechanics
Definition of 12, 55, 122
Major Poisson's Ratio 132
Mandell, J. F. 306
Manufacturing 18 - 26, 376, 424
Filament Winding 19 - 20
Molding 20 - 23
Pultrusion 22 - 23
Resin - Transfer Molding 20 - 21
Roll Forming 22
Sheet Molding 22
Tape Laying 19 - 20
Manufacturing Processes 368
Contrast Between Metals and Composites 464
Materials Selection 369, 376, 389 - 400
Factors 390
Materials Utilization Factor 33
Mathews, F. L. 422, 466
Matrix Selection Factors 392
Matrix (Material) 15, 55
Bismaleimides 394
Carbon 394
Definition of 5
Epoxy 393 - 394
Function of 15
Peek 394
Phenolics 394
Polyester 393
Polyimide 393 - 394
Polysulfone 394
Properties of 5 - 6
Restrictions on Micromechanical Behavior 124
Thermoplastic 393 - 394
Thermoset 393 - 394
Vinyl Ester 393
Volume Fraction 123
Matrix (Mathematical) 56 - 63
Addition 470
Adjoint 471
Algebra 467 - 472
Cofactor 469
Column 468
Compliance 58
Cramer's Rule 472
Definition of 467
Determinant of 469
Diagonal 468
Identity 468
Inverse 471
Inversion 471(
514 Mechanics of Composite Materials
Multiplication 470
Nonsingular 472
Principal or Main Diagonal of 468
Reversal Laws for 472
Row 468
Scalar 468
Singular 471
Solution of Linear Equations 471
Square 467
Stiffness 56, 57
Subtraction 470
Symmetric 468
Transpose 468
Unit 468
Maxima and Minima of Functions of a Single Variable 479 - 483
Maximum Strain Failure Criterion 105,
107 - 109, 112,435,453
Maximum Stress Failure
Criterion 105 - 107, 112
Mccullers, L. A. 435
Measurement of Stiffness
Cross - Beam Test 99 - 100
For a Lamina 91 - 102
Rail Sheartest 100
Torsion - Tube Test 99
Uniaxial Tension Test 93 - 98
Measurement of Strength
Cross - Beam Test 99 - 100
For a Lamina 91 - 102
Rail Shear Test 100
Torsion - Tube Test 99
Uniaxial Tension Test 93 - 98
Mechanical Behavior of Composite Materials 11 - 14
Mechanical Properties 100 - 101
Mechanics of Materials Approach to
Micromechanics
Of Stiffness 123, 126 - 137, 158 - 164
Of Strength 126, 163 - 183
Mechanistic Relationships 371, 374, 376,
386
Merit Function 377 - 378, 427, 434
Metal Matrix Materials 23, 392
Microcrack
See Cracks _
Micromechanics 393, 454, 457 - 458
Definition of 12, 122
Elasticity Approach 122, 137 - 163
Mechanics of Materials
Approach 122, 126 - 136
Of Stiffness 123
Of Strength 123
Representative Volume Element 124
Restrictions on Theory 123
Strain Assumptions 126
Mindlin, R. D. 350
Minimum Complementary Energy 138
Minimum Potential Energy 140,479
Modes of Failure 381
Mohr's Circle 477
Moire Technique 269
Moisture 359 - 360
Moisture Absorption 245 - 246, 360
Molding 20 - 23
Monoclinic Material 59
Plane Stress State 70
Strain - Stress Relations 61
Stress - Strain Relations 59
Morgan, H. S. 99, 314, 322 - 324,
361 - 362, 457
Mosesian, B. 47 - 48
Muskhelishvili, N. I. 145
- Nnanyaro, a. P. 118
Narayanaswami, R. 117
Narrow Optimum Design 378
Nastran 388 - 389
Netting Analysis 137, 253
Newton's Method 430
Nishimatsu, C. 158
Nodal Line 302
Nomex 413
Nondeterministic 374, 433 - 434
Nonlinear Behavior 458
Nonlinear Stress - Strain Behavior 362
Nonsymmetric Laminate
See Unsymmetric Laminate
Norris, C. H. 355
Northrop Grumman B - 2 45 - 46
Noton, B. R. 365,412
- 0 -
O'brien, R. 48
Olsen, F. 0. 435
Open - Versus Closed - Section
Stiffeners 405 - 407
Oplam 435, 439
Optimization 370 - 371, 376 - 377, 385,
425 - 454
Artificial Constraint 437
Brute - Force Search 428 - 429, 433,
435
Constraints 427, 434
Fundamentals of 426
Laminate 431
Mathematical 370, 428 - 430
Merit Function 427, 434
Nonlinear 429
Strength 435
Structural 426
Tsai's Laminate Ranking
Procedure 433
Orthogrid 410 - 411
Orthotropic Lamina 70 - 73
See Also Generally Orthotropic Lamina
See Also Specially Orthotropic Material
Definition of 70 - 73
Invariant Properties of 85 - 87
Stiffness in Arbitrary
Coordinates 74 - 84
Strength 88 - 118
Orthotropic Material 59
Compliances for 64
Definition of 11
Engineering Constants of 63
Invariant Properties of 85 - 87
Orthotropic Behavior 12 - 13
Plane Stress State 70
Strain - Stress Relations 61
Stress - Strain Relations 59
Orthotropic Modulus Ratio 298, 300,
311 - 312,314, 320,322,328
See Also Stiffness Ratio
Orthotropy 191,200,264,282, 336 - 337,
343 - 344,346, 348,350,455
Overdesign 383, 384, 404, 447
- Ppadding Up 409
Pagano, N. J. 85, 87, 89, 97 - 99,
119 - 120, 261,264,266, 268 - 273,
346 - 347, 348 - 350, 353, 355, 363, 365,
440 - 443, 446 - 447, 460 - 461, 466
Particulate Composite Materials 158 - 159
Definition of 2, 8
Types of 8 - 1 O
Particulate Reinforcement 2, 8 - 10, 136,
158 - 159, 163
Paul, B. 137, 143, 158 - 159, 163
Perrone, N. 364, 466
Petit, P. H. 199, 485, 489 - 494
Philips, L. N. 365
Pinckney, R. L. 334
Pipes, R. B. 99, 113 - 114, 116 - 117,
245 - 246, 261,264,266, 268 - 273, 460
Pister, K. S. 145,191,361
Plane Stress 70
Plastic Deformations 340, 362
Plastic - Based Laminates 8
Plate Aspect Ratio 279
Plate Boundary Conditions 501 - 503
Plate Buckling Equations 505 - 506
Plate Equilibrium Equations 498 - 505
Plate Vibration Equations 506
Plates, Laminated
See Laminated Plates
Ply Drops 409
Plywood 2
Poisson's Ratios 13, 63 - 67, 84, 101
Lnutlx 515
Apparent 140 - 143
Apparent for a Lamina 132 - 133,
142 - 143, 148
Definition of 64
Effect on Transverse Modulus 131
Restrictions on 67 - 70
Polymer Matrix Materials 392
Polymers
Branched 5
Cross - Linked 5
Linear 5
Postcuring Shapes of Laminates 356 - 359
Post, D. 269
Potential Energy 357
Preliminary Design - Analysis 387 - 388
Principal Material Coordinates
Definition of 59
Shear Strength in 89
Principal Material Directions 59
See Also Principal Material Coordinates
Definition of 59
Determination of 67
Nonalignment With Coordinate Directions 74
Principle of Minimum Complementary Energy 138
Principle of Minimum Potential
Energy 140, 479
Principle of Stationary Potential
Energy 292, 479
Pultrusion 22 - 23
- Qquasi - Isotropic Laminate
- Rradiation 361
Rail Shear Test 100
Rayleigh - Ritz Method 289, 292 - 294, 306,
318,328
Rc7 435
Reciprocal Relations 65, 68, 72, 80, 95
Generalized Betti's Law 66
Reddy,j. N. 91,277
Reduced Bending Stiffness
Approximation 328 - 329, 456
Reduced Stiffnesses 71, 77, 191
Reed, D. L. 335
Regular Antisymmetric Angle - Ply
Laminate 217, 232(
516 Mechanlc:s of Composite Materials
Regular Antisymmetric Cross - Ply
Laminate 216
Regular Laminate 210 - 212, 216 - 217, 219
Regular Symmetric Angle - Ply
Laminate 212, 232
Regular Symmetric Cross - Ply
Laminate 210
Reifsnider, K. L. 333
Reissner Variational Theorem 355
Reissner, E. 191,350,355,419
Representative Volume Element 124 - 134,
145 - 146, 168, 172
Definition of 124
Resin - Transfer Molding 20 - 21
Reuter Matrix 75 - 76, 78
Reuter, R. C. 75
Riley, M. B. 147
Roll - Forming 22
Rosen, B. W. 4, 143 - 144, 147, 163,
168 - 172, 1n. 101 - 102
Rule of Mixtures 127, 132, 135, 138, 144,
149, 151, 156, 159
Rutan Voyager 48
- Ssaint - Venant, Barre De
End Effects 97
Semi - Inverse Method 145
Salkind, M. J. 333, 335, 362
Savin, G. N. 336
Schapery, R. A. 362
Schmit, L. A. 431, 447
Schuerch, H. 182 - 183
Schwartzkopf, P. 158
Schwartz,h.s. 120
Schwartz, M. M. 394
Schwartz,r. T. 120
Self - Consistent Model 137, 147, 151
Semi - Inverse Method 145
Sendeckyj, G.y. 118, 137, 147, 158
Sensitivity Studies 371, 378
Separation of Variables 289, 291
Serafini, T. T. 345
Shear Deformation Theory 350 - 355
Shear Moduli
Shear Stiffness
Shear Strength 88, 91, 96 - 101, 115
Shear - Extension Coupling
Shear - Shear Coupling 80
Sheet Molding Compound 22
Shells, Laminated 361
Shen, C. H. 245
Shockey, D. 99
Shtrikman, S. 143, 159
Sierakowski, R. L. 2n
Signorelli, R. A. 365
Sih, G. C. 345
Sims, D. F. 362
Skew Plates 293 - 307
Softening Strip Concept 338 - 339
Solution Techniques 288 - 289
Complex Variable Mapping 145
Fin!te Differences 145, 266 - 267, 289
Finite Elements 125,145,289
Galerkin Method 289
Rayleigh - Ritz Method 289
Semi - Inverse Method 145
Separation of Variables 289
Space Effects 361
Specially Orthotropic Lamina 76, 78
See Also Orthotropic Lamina
Specially Orthotropic Laminate 214,
278 - 279, 290 - 291, 303 - 305, 315 - 317
Specific Stiffness 3 - 4, 27 - 31
Specific Strength 3 - 4, 27 - 31
Springer, G. S. 245, 276, 360
Stacking Sequence 219, 240, 272
Stansbarger, D. L. 100
Stationary Potential Energy 292, 479
Stavsky, Y. 191, 355
Stiffened Structures 400, 414
See Also Stiffeners
Advantages of Composite
Materials 401
Honeycomb Core 414 - 415, 421
Isogrid 411
Metal Versus Composite 402
Optimization 402
Orthogrid 410 - 411
Sandwich Core 414
Shells 361
Stiffener Design 407 - 410
Stiffeners 379,400
Design 407 - 410
Design Parameters 407
Eccentricity 408
Embedded Stiffening Strap 404
Hat 405 - 406
Manufacturing 403
Open - Versus Closed - Section 405
Optimum Design 404
Sandwich - Blade 405 - 406
Types 403
Stiffening Strip Concept 338 - 339
Stiffness 2, 26 - 31, 381,390,398,423
Stiffness in Fiber Direction 88
Stiffness Ratio 225
See Also Orthotropic Modulus Ratio
Stiffness Tensor 91, 102
Stiffness Transverse· to Fiber Direction 88
Stiffness - Sensitive Structures 386
Stiffnesses
See Also Coupling
Bending 198 - 199
Bending - Extension 198
Comparison of Measured and Predicted 222 - 237
Definition of 56
Elastic Constants 58
Extensional 198 - 199
For Bending - Extension Coupling 199
In Fiber Direction 88, 91, 93 - 95
Inversion of 222 - 224
Laminate 198 - 237
Measurement of 91 - 102, 229 - 232,
235 - 236
Mnemonic Notation for 58
Of Anisotropic Layer 205 - 206
Of Generally Orthotropic Layer 205
Of Isotropic Layer 203 - 204
Of Specially Orthotropic Layer 204 - 205
Reduced 191
Relation to Compliances for Orthotropic
Materials 66
Restrictions on 68
Shear 88, 91, 96 - 101, 115
Special Cases for 203 - 222
Symmetry of 58
Transformation of N, 85
Transformed Reduced 191
Transverse to Fiber Direction 88, 91,
95 - 96
Unequal in Tension and
Compression 89 - 91
Stinchcomb, W. W. 333
Strain Distribution 281
Strain Energy 138 - 141, 340 - 341, 345
Strain - Displacement Relations 56, 193,
265
Strain - Energy - Release Rate 340 - 342
Strain - Stress Relations
Anisotropic 60
Isotropic 62
Monoclinic 61
Orthotropic 61
Plane Stress (Orthotropic) 71
Transversely Isotropic 61
Strains
Engineering Shear Strain 56 - 57, 75
Expansional 242 - 246
Linear Strain - Displacement
Relations 56
Principal 88
Tensor Shear Strain 56 - 57, 75
Transformation of 7 4
Volumetric Strain 67
Street, K. N. 365
Strength 2, 26 - 31, 390, 398, 423
See Also Anisotropic Lamina
See Also Generally Orthotropic Lamina
See Also Orthotropic Lamina
See Also Specially Orthotropic Lamina
Analogy to Plate Buckling · 238
Angle - Ply Laminate 255 - 258
111dex 517
Axial 88
Cross - Ply Laminate 246 - 255
Experimental Determination
Of 91 - 102
Fatigue 272, 333 - 336, 339
In Fiber Direction 88, 91, 93 - 95
Longitudinal 88
Of a Laminate 237 - 260
Of an Orthotropic Lamina 88 - 118
Shear 88, 91, 96 - 101, 115
Transverse to Fiber Direction 88, 91,
95 - 96
Unequal in Tension and
Compression 89 - 91, 115
Strength in Fiber Direction 88
Strength Tensor 91, 102, 115
Strength Transverse to Fiber Direction 88
Stress Concentration 409
Stress Concentration Factor 336 - 339,
342,383
Stress Distribution 281
Stress - Strain Behavior
Lamina 191
Nonlinear 454, 458
Stress - Strain Relations 118
Anisotropic 56
Compliances in 118
Engineering Constants in 118
For a Generally Orthotropic Lamina 77
For a Lamina of Arbitrary
Orientation 74 - 85
For a Specially Orthotropic Lamina 76
Isotropic 60
Monoclinic 59
Orthotropic 59
Plane Stress (Orthotropic) 71
Stiffnessesin 118
Thermal 242 - 244
Transformed 7 4
Transversely Isotropic 59
Stresses
Hygroscopic 245 - 246
Intertaminar 260 - 275
Moisture 245 - 246
Principal 88
Thermal 242 - 260
Transformation of 7 4
Strong Design Drivers 378
Structural Configuration 426
Structural Design Process 368, 370,
372 - 389
Structural Optimization 426
Structural Optimization Techniques 447
Structural Polymers
Thermoplastic - Matrix Materials 5,
25 - 26
Thermoset - Matrix Materials 5, 23
Structural Reconfiguration 380, 383 - 384,
414 - 417
Structural Response Parameters 381 - 382
Structural Synthesis 428(
518 Mecha~ .,f Composite Materials
Supersonic Transport 38, 49
Sutton, W. H. 4
Swedlow, J. L. 345
Symmetric Laminate 206 - 214
Angle - Ply 212 - 213, 233, 291 - 295,
306 - 307
Bending of 290 - 295
Buckling of 303 - 307
Cross - Ply 210 - 211, 225, 354
Regular 210 - 212
Stiffnesses 206 - 214
Vibration 315 - 318
With Anisotropic Layers 213 - 214
With Generally Orthotropic
Layers 211 - 213
With Isotropic Layers 207 - 209
With Specially Orthotropic
Layers 209 - 211, 290 - 291
- Ttailoring of Composite Materials 12, 18,
378
Talreja, R. 335
Tape Laying 19 - 20
Taylor Series 480 - 481
Taylor, R. L. 361
Technical Constants 63
See Also Engineering Constants
Temperature Effects 242 - 260, 360
Tennyson, R. C. 118
Tensors 467, 472 - 477
Cartesian 472
Contracted Notation for 475 - 476
Direction Cosines for 473
Dummy Index 473
Index Notation 472
Matrix Form of 476 - 477
Order of 472, 474
Range Convention for 473
Scalar 474
Summation Convention for 473
Transformation of 472 - 477
Vector 474
Tetelman, a. S. 345
Thermal Conductivity 2
Thermal Expansion 242, 390
Thermal Stresses 242 - 260, 356
Coefficient of Thermal Expansion 242
Equivalent Mechanical Loads 244
Free Thermal Strain 242
Thermal Coupling 252 - 253, 258
Thermal Forces 243, 356
Thermal Moments 244, 356
Thermoplastic - Matrix Materials 5, 25 - 26
Thermoset - Matrix Materials 5, 23
Thomas, R. L. 152
Tirnoshenko, S. P. 174 - 175, 283, 289,
301,506
Torsion - Tube Test 99
Total Potential Energy 357
Trade Studies 388
Trade - Off 375, 390, 463, 465
Transformation of Stiffnesses 77, 85
Transformation of Strains 74
Transformation of Stresses 74
Transformed Reduced Stiffnesses 77, 85,
97, 191
Transverse Load 289 - 290, 296, 353 - 354
Transverse Shearing Effects 345 - 355,
460 - 461
Transverse Shearing Stresses 454, 505
Transverse Stiffness 91, 95, 101,
129 - 131, 148
Transverse Strength 88, 91, 95, 101
Transversely Isotropic Material 59
Plane Stress State 70
Strain - Stress Relations 61
Stress - Strain Relations 59
Triclinic Material 58
See Also Anisotropy
Trifurcation 358
Tsai - Hill Failure Criterion
Tsai - Wu Tensor Failure Criterion
Tsai
- Uunderdesign 383
Uniaxial Tension Test 93 - 98
Unidirectionally Reinforced Lamina 15,
27 - 28, 55, 70, 73, 108
See Also Orthotropic Lamina
Fundamental Strengths of 88 - 102
Invariant Properties of 85 - 87
Macromechanical Behavior 55 - 119
Micromechanical Behavior 121 - 185
Representative Volume Element 124
Strength of 88 - 102, 163 - 185
Compressive 171 - 185
Tensile 164 - 171
Unsymmetric Laminate 206,214,
218 - 219, 323 - 327, 356 - 359, 362
Cross - Ply 356 - 359
Postcuring Shapes 356 - 359
- Vvan Cleave, R. R. 47
Van Hamersveld, J. 47
Variations in Displacements 506
Vasiliev, V. V. 277
Vibration 317, 381 - 382, 427
Frequencies 316 - 317, 319'.323, 327,
360 - 361
Mode Shapes 316 - 317
Vibration of Laminated Plates 277 - 279,
288, 315 - 322
Antisymmetric Angle - Ply
Laminates 320 - 322
Antisymmetric Cross - Ply
Laminates 318 - 320
Boundary Conditions 288
Governing Equations 288
Solution Techniques 288 - 289
Specially Orthotropic
Laminates 315 - 317
Symmetric Angle - Ply
Laminates 317 - 318
Unsymmetric Cross - Ply
Laminates 327
Vinson, J. R. 245 - 246, 277
Viscoelastic Behavior 17, 362
Volume Fraction 123
Von Mises, R. 104
Vought a - 7 Speedbrake 40 - 41
Vought S - 3a Spoiler 42 - 43
- Wwaddoups, M. E. 99, 306, 345, 435
Wang, a. S. D. 348
Wang,j. T.s. 289
Wave Propagation 362
Weak Design Drivers 378
Weibull Distribution 169
Weight 2, 36 - 37, 424
Index 519
Weight - Sensitive Structures 386, 390
Wendt, F. W. 364, 466
Whiskers 15
Definition of 4
Properties of 4
Whitney, J.m.
Wide Optimum Design 378
Wilkins, D. J. 335
Woinowsky - Krieger, S. 283, 289
Woven Lamina 15, 125
Wu, E. M. 105, 114 - 117, 339 - 340,
343 - 344
- Vyang, P. C. 355
Young's Moduli 13, 63, 84, 123, 143
Apparent 138 - 143
Apparent for a Lamina 127 - 131, 143
For Boron - Epoxy 69
Restrictions on 68
Yurenka, S. 363
- Zzhang, G. 183
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