 | Vasiliev V.V. Advanced mechanics of composite materials and structural elements / V.V.Vasiliev, E.V.Morozov. - 3rd ed. - Kidlington, Oxford: Elsevier, 2013. - xiii, 818 p.: ill. - Incl. bibl. ref. - Auth., sub. ind.: p.797-818. - ISBN 978-0-08-098231-1
Шифр: (И/Ж-V30) 02
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Preface to the Third Edition ................................... xi
CHAPTER 1 Introduction ......................................... 1
1.1 Structural Materials ....................................... 1
1.2 Composite Materials ........................................ 9
1.2.1 Fibers for Advanced Composites ...................... 9
1.2.2 Matrix Materials ................................... 15
1.2.3 Processing ......................................... 21
1.3 References ................................................ 27
CHAPTER 2 Fundamentals of Mechanics of Solids ................. 29
2.1 Stresses .................................................. 29
2.2 Equilibrium Equations ..................................... 31
2.3 Stress Transformation ..................................... 32
2.4 Principal Stresses ........................................ 34
2.5 Displacements and Strains ................................. 35
2.6 Transformation of Small Strains ........................... 38
2.7 Compatibility Equations ................................... 39
2.8 Admissible Static and Kinematic Fields .................... 40
2.9 Constitutive Equations for an Elastic Solid ............... 40
2.10 Formulations of the Problem ............................... 46
2.11 Variational Principles .................................... 47
2.11.1 Principle of Minimum Total Potential Energy ........ 48
2.11.2 Principle of Minimum Strain Energy ................. 49
2.11.3 Mixed Variational Principles ....................... 50
2.12 Reference ................................................. 51
CHAPTER 3 Mechanics of a Unidirectional Ply ................... 53
3.1 Ply Architecture .......................................... 53
3.2 Fiber-Matrix Interaction .................................. 57
3.2.1 Theoretical and Actual Strength .................... 57
3.2.2 Statistical Aspects of Fiber Strength .............. 61
3.2.3 Stress Diffusion in Fibers Interacting through
the Matrix ......................................... 65
3.2.4 Fracture Toughness ................................. 78
3.3 Micromechanics of a Ply ................................... 80
3.4 Mechanical Properties of a Ply Under Tension, Shear, and
Compression ............................................... 95
3.4.1 Longitudinal Tension ............................... 95
3.4.2 Transverse Tension ................................. 99
3.4.3 In-Plane Shear .................................... 104
3.4.4 Longitudinal Compression .......................... 107
3.4.5 Transverse Compression ............................ 115
3.5 Hybrid Composites ........................................ 116
3.6 Composites with High Fiber Fraction ...................... 119
3.7 Phenomenological Homogeneous Model of a Ply .............. 122
3.8 References ............................................... 123
CHAPTER 4 Mechanics of a Composite Layer ..................... 125
4.1 Isotropic Layer .......................................... 125
4.1.1 Linear Elastic Model .............................. 125
4.1.2 Nonlinear Models .................................. 129
4.2 Unidirectional Orthotropic Layer ......................... 144
4.2.1 Linear Elastic Model .............................. 144
4.2.2 Nonlinear Models .................................. 147
4.3 Unidirectional Anisotropic Layer ......................... 152
4.3.1 Linear Elastic Model .............................. 152
4.3.2 Nonlinear Models .................................. 169
4.4 Orthogonally Reinforced Orthotropic Layer ................ 169
4.4.1 Linear Elastic Model .............................. 170
4.4.2 Nonlinear Models .................................. 173
4.4.3 Two-Matrix Composites ............................. 187
4.4.4 Composites with Controlled Cracks ................. 191
4.5 Angle-Ply Orthotropic Layer .............................. 196
4.5.1 Linear Elastic Model .............................. 196
4.5.2 Nonlinear Models .................................. 200
4.5.3 Free-Edge Effects ................................. 211
4.6 Layer Made by Angle-ply Circumferential Winding .......... 216
4.7 Fabric Layers ............................................ 223
4.8 Lattice Layer ............................................ 230
4.9 Spatially Reinforced Layers and Bulk Materials ........... 232
4.10 References ............................................... 240
CHAPTER 5 Mechanics of Laminates ............................. 243
5.1 Stiffness Coefficients of a Nonhomogeneous Anisotropic
Layer .................................................... 243
5.2 Stiffness Coefficients of a Homogeneous Layer ............ 254
5.3 Stiffness Coefficients of a Laminate ..................... 255
5.4 Symmetric Laminates ...................................... 257
5.5 Engineering Stiffness Coefficients of Orthotropic
Laminates ................................................ 260
5.6 Quasi-Homogeneous Laminates .............................. 272
5.6.1 Laminate Composed of Identical Homogeneous
Layers ............................................ 272
5.6.2 Laminate Composed of Inhomogeneous Orthotropic
Layers ............................................ 273
5.6.3 Laminate Composed of Angle-Ply Layers ............. 274
5.6.4 Fiber Metal Laminates ............................. 275
5.7 Quasi-Isotropic Laminates in the Plane Stress State ...... 277
5.8 Antisymmetric Laminates .................................. 284
5.9 Sandwich Structures ...................................... 288
5.10 Coordinate of the Reference Plane ................... 292
5.11 Stresses in Laminates ............................... 295
5.12 References .......................................... 296
CHAPTER 6 Failure Criteria and Strength of Laminates ......... 299
6.1 Failure Criteria for an Elementary Composite Layer or
Ply ...................................................... 300
6.1.1 Maximum Stress and Strain Criteria ................ 301
6.1.2 Approximation Strength Criteria ................... 309
6.1.3 Tensor Strength Criteria .......................... 313
6.1.4 Interlaminar Strength ............................. 320
6.2 Practical Recommendations ................................ 321
6.3 Examples ................................................. 322
6.4 Allowable Stresses for Laminates Consisting of
Unidirectional Plies ..................................... 327
6.5 Progressive Failure: Modeling and Analysis ............... 332
6.5.1 Constitutive Equations ............................ 333
6.5.2 Plastic Model ..................................... 335
6.5.3 Damage Model ...................................... 337
6.5.4 Numerical Implementation .......................... 340
6.5.5 Numerical Analyses ................................ 343
6.6 References .......................................... 350
CHAPTER 7 Environmental, Special Loading, and
Manufacturing Effects ......................................... 353
7.1 Temperature Effects ...................................... 353
7.1.1 Thermal Conductivity .............................. 353
7.1.2 Thermoelasticity .................................. 358
7.2 Hygrothermal Effects and Aging ........................... 368
7.3 Time-Dependent Loading Effects ........................... 376
7.3.1 Viscoelasticity ................................... 376
7.3.2 Durability ........................................ 388
7.3.3 Cyclic Loading .................................... 392
7.3.4 Impact Loading .................................... 401
7.4 Manufacturing Effects .................................... 418
7.4.1 Circumferential Winding and Tape Overlap Effect ... 418
7.4.2 Warping and Bending of Laminates in Fabrication
Process ........................................... 424
7.4.3 Shrinkage Effects and Residual Strains ............ 428
7.5 References ............................................... 432
CHAPTER 8 Laminated Composite Beams and Columns .............. 435
8.1 Basic Equations .......................................... 435
8.2 Stiffness Coefficients ................................... 442
8.3 Bending of Laminated Beams ............................... 444
8.4 Nonlinear Bending ........................................ 450
8.5 Buckling of Composite Columns ............................ 457
8.6 Free Vibrations of Composite Beams ....................... 459
8.7 Refined Theories of Beams and Plates ..................... 464
8.8 References ............................................... 485
CHAPTER 9 Laminated Composite Plates ......................... 487
9.1 Equations of the Theory of Anisotropic Laminated Plates .. 487
9.2 Equations for the Orthotropic Plates with Symmetric
Structure ................................................ 493
9.3 Analysis of the Equations of Plate Theory for
Transversely Isotropic Plates ............................ 495
9.3.1 Classical Plate Theory ............................ 496
9.3.2 Theory of Shear Deformable Plates ................. 502
9.4 Bending of Orthotropic Symmetric Plates .................. 519
9.4.1 Exact Solutions of Classical Plate Theory ......... 519
9.4.2 Approximate Solutions for Classical Plate Theory .. 534
9.4.3 Shear Deformable Orthotropic Symmetric Plates ..... 537
9.5 Buckling of Orthotropic Symmetric Plates ................. 545
9.5.1 Classical Plate Theory ............................ 545
9.5.2 Theory of Shear Deformable Plates ................. 556
9.6 Postbuckling Behavior of Orthotropic Symmetric Plates
Under Axial Compression .................................. 559
9.7 Generally Laminated Plates ............................... 565
9.7.1 Bending of Unsymmetric Plates ..................... 565
9.7.2 In-Plane Loading .................................. 570
9.7.3 Shear Deformable Unsymmetrically Laminated
Plates ............................................ 576
9.8 References ............................................... 580
CHAPTER 10 Thin-Walled Composite Beams ........................ 585
10.1 Geometry of the Beam Cross Section ....................... 587
10.2 The Equations of Membrane Shell Theory ................... 589
10.3 Assumptions of Composite Beam Theory ..................... 590
10.4 Free Bending and Torsion of Thin-walled Beams with
a Closed Cross-sectional Contour ......................... 593
10.4.1 Axial Strain and Stress Resultant ................. 593
10.4.2 Shear Strain and Stress Resultant ................. 597
10.4.3 Stresses in the Plies of Composite Beams .......... 600
10.4.4 Determination of Displacements .................... 603
10.4.5 Warping Function .................................. 605
10.4.6 Beams with Circular and Rectangular Cross
Sections .......................................... 606
10.4.7 Shear and Twist Center ............................ 617
10.4.8 Anisotropic Thin-Walled Beams ..................... 622
10.4.9 Beams Stiffened with Axial Ribs ................... 635
10.4.10 Beams Loaded with Body and Surface Forces ........ 643
10.4.11 Restrained Torsion and Bending of Beams with
Closed Cross-Sectional Contours .................. 645
10.5 Beams with Multi-cell Cross-sectional Contours ........... 652
10.6 Beams with Open Cross-Sectional Contours ................. 657
10.6.1 Transverse Bending ................................ 657
10.6.2 Free Torsion of Beams with Open Cross-Sectional
Contours .......................................... 662
10.6.3 Restrained Torsion of Beams with Open Cross-
Sectional Contours ................................ 677
10.7 References ............................................... 683
CHAPTER 11 Circular Cylindrical Shells ........................ 685
11.1 Governing Equations and Applied Shell Theories ........... 686
11.2 Cylindrical Shells whose Stress-Strain State does not
Depend on the Axial Coordinate ........................... 692
11.2.1 Circular Rings .................................... 692
11.2.2 Infinitely Long Cylindrical Panel ................. 698
11.3 Axisymmetric Deformation of Cylindrical Shells ........... 703
11.3.1 Linear Theory of Shear Deformable Shells .......... 706
11.3.2 Linear Classical Shell Theory ..................... 706
11.3.3 Nonlinear Classical Theory ........................ 707
11.3.4 Nonlinear Membrane Theory ......................... 707
11.3.5 Examples .......................................... 707
11.3.6 Anisotropic Shells ................................ 713
11.4 General Loading Case ..................................... 714
11.4.1 Classical Shell Theory ............................ 714
11.4.2 Engineering Shell Theory .......................... 717
11.4.3 Semi-Membrane Shell Theory ........................ 717
11.4.4 Membrane Shell Theory ............................. 722
11.4.5 Shear Deformable Shell Theory ..................... 722
11.5 Buckling of Cylindrical Shells Under Axial Compression ... 725
11.5.1 Column-Type Buckling .............................. 725
11.5.2 Axisymmetric Buckling Mode ........................ 726
11.5.3 Nonsymmetric Buckling Mode ........................ 732
11.6 Buckling of Cylindrical Shells Under External Pressure ... 738
11.6.1 Simply Supported Shells ........................... 739
11.6.2 Infinitely Long Shells ............................ 740
11.6.3 Hydrostatic Pressure .............................. 741
11.7 References ............................................... 742
CHAPTER 12 Optimal Composite Structures ....................... 745
12.1 Optimal Fibrous Structures ............................... 745
12.2 Composite Laminates of Uniform Strength .................. 752
12.3 Optimal Design of Laminates .............................. 758
12.3.1 Optimization Under Strength Constraints ........... 760
12.3.2 Optimization Under Strength and Buckling
Constraints ....................................... 765
12.4 Application to Optimal Composite Structures .............. 766
12.4.1 Composite Pressure Vessels ........................ 766
12.4.2 Spinning Composite Disks .......................... 779
12.4.3 Anisogrid Composite Lattice Structures ............ 785
12.5 References ............................................... 795
Author Index .................................................. 797
Subject Index ................................................. 801
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