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ОбложкаVasiliev 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
 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
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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