Advanced Mechanics of Composite Materials and Structures

Opis

Advanced Mechanics of Composite Materials and Structures analyzes contemporary theoretical models at the micro- and macro levels of material structure. Its coverage of practical methods and approaches, experimental results, and optimization of composite material properties and structural component performance can be put to practical use by researchers and engineers.

The fourth edition has been updated to reflect new manufacturing processes (such as 3D printing of two matrix composite structural elements) and new theories developed by the authors. The authors have expanded the content of advanced topic areas with new chapters on axisymmetric deformation of composite shells of revolution, composite pressure vessels, and anisogrid composite lattice structures. This revision includes enhanced sections on optimal design of laminated plates and additional examples of the finite element modelling of composite structures and numerical methods.

Advanced Mechanics of Composite Materials and Structures, Fourth edition is unique in that it addresses a wide range of advanced problems in the mechanics of composite materials, such as the physical statistical aspects of fiber strength, stress diffusion in composites with damaged fibers, nonlinear elasticity, and composite pressure vessels to name a few. It also provides the foundation for traditional basic composite material mechanics, making it one of the most comprehensive references on this topic.

Presents advanced material on composite structures, including chapters on composite pressure vessels and axisymmetric deformation of composite shells of revolution
Provides the applications of composite materials to spacecraft, aircraft and marine included throughout
Practical examples of analysis and design of real composite structural components

Spis treści

Front Cover 2
Advanced Mechanics of Composite Materials and Structures 5
Copyright Page 6
Contents 7
Preface 15
Introduction 19
1 Mechanics of a Unidirectional Ply 29
- 1.1 Ply Architecture 29
- 1.2 Fiber–Matrix Interaction 33
  - 1.2.1 Theoretical and Actual Strength 33
  - 1.2.2 Statistical Aspects of Fiber Strength 37
  - 1.2.3 Stress Diffusion in Fibers Interacting Through the Matrix 41
  - 1.2.4 Fracture Toughness 52
- 1.3 Micromechanics of a Ply 55

Front Cover 2
Advanced Mechanics of Composite Materials and Structures 5
Copyright Page 6
Contents 7
Preface 15
Introduction 19
1 Mechanics of a Unidirectional Ply 29
- 1.1 Ply Architecture 29
- 1.2 Fiber–Matrix Interaction 33
  - 1.2.1 Theoretical and Actual Strength 33
  - 1.2.2 Statistical Aspects of Fiber Strength 37
  - 1.2.3 Stress Diffusion in Fibers Interacting Through the Matrix 41
  - 1.2.4 Fracture Toughness 52
- 1.3 Micromechanics of a Ply 55
- 1.4 Mechanical Properties of a Ply Under Tension, Shear, and Compression 70
  - 1.4.1 Longitudinal Tension 70
  - 1.4.2 Transverse Tension 74
  - 1.4.3 In-Plane Shear 79
  - 1.4.4 Longitudinal Compression 82
  - 1.4.5 Transverse Compression 89
- 1.5 Interlaminar Stiffness and Strength 90
- 1.6 Hybrid Composites 92
- 1.7 Composites With High Fiber Fraction 96
- 1.8 Limitations of the Phenomenological Homogeneous Model of a Ply 98
- References 99
2 Mechanics of a Composite Layer 103
- 2.1 Isotropic Layer 104
  - 2.1.1 Linear Elastic Model 104
  - 2.1.2 Nonlinear Models 107
- 2.2 Unidirectional Orthotropic Layer 121
  - 2.2.1 Linear Elastic Model 123
  - 2.2.2 Nonlinear Models 124
- 2.3 Unidirectional Anisotropic Layer 128
  - 2.3.1 Linear Elastic Model 129
  - 2.3.2 Nonlinear Models 145
- 2.4 Orthogonally Reinforced Orthotropic Layer 147
  - 2.4.1 Linear Elastic Model 148
  - 2.4.2 Nonlinear Models 150
  - 2.4.3 Composites With Controlled Cracks 164
  - 2.4.4 Two-Matrix Composites 166
  - 2.4.5 Two-Matrix Composite Made by Three-Dimensional Printing 172
- 2.5 Angle-Ply Orthotropic Layer 175
  - 2.5.1 Linear Elastic Model 175
  - 2.5.2 Nonlinear Models 179
  - 2.5.3 Free-Edge Effects 191
- 2.6 Layer Made by Angle-Ply Circumferential Winding 195
- 2.7 Fabric Layers 201
- 2.8 Spatially Reinforced Layers and Bulk Materials 208
- References 215
3 Mechanics of Laminates 219
- 3.1 Stiffness Coefficients of a Nonhomogeneous Anisotropic Layer 219
- 3.2 Stiffness Coefficients of a Homogeneous Layer 229
- 3.3 Stiffness Coefficients of a Laminate 230
- 3.4 Symmetric Laminates 232
- 3.5 Engineering Stiffness Coefficients of Orthotropic Laminates 234
- 3.6 Quasi-Homogeneous Laminates 246
  - 3.6.1 Laminate Composed of Identical Homogeneous Layers 247
  - 3.6.2 Laminate Composed of Inhomogeneous Orthotropic Layers 247
  - 3.6.3 Laminate Composed of Angle-Ply Layers 248
  - 3.6.4 Fiber Metal Laminates 249
- 3.7 Quasi-Isotropic Laminates in the Plane Stress State 251
- 3.8 Antisymmetric Laminates 257
- 3.9 Sandwich Structures 263
- 3.10 Coordinate of the Reference Plane 264
- 3.11 Stresses in Laminates 267
- References 269
4 Failure Criteria and Strength of Laminates 271
- 4.1 Failure Criteria for an Elementary Composite Layer or Ply 272
  - 4.1.1 Maximum Stress and Strain Criteria 275
  - 4.1.2 Approximation Strength Criteria 281
  - 4.1.3 Tensor Strength Criteria 285
  - 4.1.4 Interlaminar Strength 292
- 4.2 Practical Recommendations 293
- 4.3 Examples 295
- 4.4 Allowable Stresses for Laminates Consisting of Unidirectional Plies 300
- 4.5 Progressive Failure: General Approach to Modeling and Analysis 304
  - 4.5.1 Constitutive Equations 306
  - 4.5.2 Plastic Model 307
  - 4.5.3 Damage Model 309
    - 4.5.3.1 Damage Initiation and Propagation Criteria 309
    - 4.5.3.2 Damage Evolution 310
  - 4.5.4 Numerical Implementation 312
    - 4.5.4.1 Integration Algorithm 312
    - 4.5.4.3 Viscous Regularization 313
    - 4.5.4.2 Consistent Tangent Stiffness Matrix 313
    - 4.5.4.4 Computational Procedure 314
  - 4.5.5 Numerical Analyses 315
    - 4.5.5.1 Analysis of AS4/3501-6 Double-Notched Laminate 315
    - 4.5.5.2 AS4/PEEK [±45°]2s Composite Laminate 319
  - References 320
- 5 Environmental, Special Loading, and Manufacturing Effects 323
  - 5.1 Temperature Effects 323
    - 5.1.1 Thermal Conductivity 323
    - 5.1.2 Thermoelasticity 328
  - 5.2 Hygrothermal Effects and Aging 338
  - 5.3 Time-dependent Loading Effects 346
    - 5.3.1 Viscoelastisity 346
    - 5.3.2 Durability 358
    - 5.3.3 Cyclic Loading 362
    - 5.3.4 Impact Loading 369
  - 5.4 Manufacturing Effects 388
    - 5.4.1 Porosity Effect 388
    - 5.4.2 Tape Overlap Effect 388
    - 5.4.3 Warping and Bending of Laminates in Fabrication Process 394
    - 5.4.4 Shrinkage Effects and Residual Strains 398
  - References 401
- 6 Laminated Composite Beams and Columns 405
  - 6.1 Basic Equations 405
  - 6.2 Stiffness Coefficients 412
  - 6.3 Bending of Laminated Beams 414
  - 6.4 Nonlinear Bending 420
  - 6.5 Buckling of Composite Columns 426
  - 6.6 Free Vibrations of Composite Beams 429
  - 6.7 Refined Theories of Beams and Plates 434
    - 6.7.1 First-Order Theory 435
    - 6.7.2 Higher-Order theories 436
    - 6.7.3 Consistency Conditions 441
    - 6.7.4 Theory of Elasticity Solution 441
    - 6.7.5 Nonclassical Elasticity Solution 447
  - 6.8 Laminated Beams 456
  - References 462
- 7 Laminated Composite Plates 465
  - 7.1 Equations of the Theory of Anisotropic Laminated Plates 465
  - 7.2 Equations for the Orthotropic Plates with Symmetric Structure 471
  - 7.3 Analysis of Plate Theory for Transversely Isotropic Plates 473
    - 7.3.1 Classical Plate Theory 474
    - 7.3.2 Theory of Shear Deformable Plates 480
      - 7.3.2.1 Theory equations 480
      - 7.3.2.2 Bending problem 484
      - 7.3.2.3 Torsion problem 496
    - 7.4 Bending of Orthotropic Symmetric Plates 503
      - 7.4.1 Exact Solutions of Classical Plate Theory 504
        
        7.4.1.1 Simply supported plates 504
        
        7.4.1.2 Plates simply supported at opposite edges 507
        
        7.4.1.3 Clamped plates 510
      - 7.4.2 Approximate Solutions for Classical Plate Theory 517
      - 7.4.3 Shear Deformable Orthotropic Symmetric Plates 520
    - 7.5 Buckling of Orthotropic Symmetric Plates 527
      - 7.5.1 Classical Plate Theory 528
      - 7.5.2 Theory of Shear Deformable Plates 539
    - 7.6 Postbuckling Behavior of Orthotropic Symmetric Plates Under Axial Compression 542
    - 7.7 Generally Laminated Plates 546
      - 7.7.1 Bending of Unsymmetric Plates 548
      - 7.7.2 In-Plane Loading 552
      - 7.7.3 Shear Deformable Unsymmetrically Laminated Plates 557
    - 7.8 Optimal Design of Laminated Composite Plates 561
      - 7.8.1 Optimal Fibrous Structures 561
      - 7.8.2 Composite Laminates of Uniform Strength 566
      - 7.8.3 Optimal Design of Laminated Plates 572
        
        7.8.3.1 Optimization under strength constraints 573
        
        7.8.3.2 Optimization under strength and buckling constraints 578
      - 7.9 Circular Composite Plates and Disks 580
        
        7.9.1 Governing Equations 580
        
        7.9.2 Plane Stress State of Symmetrically Laminated Plates 581
        
        7.9.3 Optimal Fibrous Structure of a Spinning Disk 585
        
        7.9.4 Bending of Plates with Symmetrically Laminated Structure 590
        
        7.9.5 Plates with Nonsymmetrically Laminated Structure 595
        
        7.9.6 Circular Plates Orthotropic in Cartesian Coordinates 598
      - References 598
    - 8 Equations of the Applied Theory of Thin-Walled Composite Structures 603
      - 8.1 Geometry of the Structure 603
      - 8.2 Strain-Displacement Equations 605
      - 8.3 Constitutive Equations 607
      - 8.4 Equilibrium Equations 609
      - 8.5 Boundary Conditions 611
      - 8.6 Classical Shell Theory 611
      - 8.8 Membrane Theory 612
      - 8.7 Engineering Theory 612
      - 8.9 Nonlinear Theories 613
      - 8.10 Buckling Equations 615
      - 8.11 Equations of Dynamics 616
      - References 617
    - 9 Thin-Walled Composite Beams 619
      - 9.1 Geometry of the Beam Cross-Section 619
      - 9.2 Basic Equations 623
      - 9.3 Assumptions of Composite Beam Theory 624
      - 9.4 Free Bending and Torsion of Thin-Walled Beams With a Closed Cross-Sectional Contour 627
        
        9.4.1 Axial Strain and Stress Resultant 628
        
        9.4.2 Shear Strain and Stress Resultant 631
        
        9.4.3 Stresses in the Plies of Composite Beams 634
        
        9.4.4 Determination of Displacements 637
        
        9.4.5 Warping Function 639
        
        9.4.6 Beams With Circular and Rectangular Cross-Sections 640
        
        9.4.7 Shear and Twist Center 650
        
        9.4.8 Anisotropic Thin-Walled Beams 655
        
        9.4.9 Beams Stiffened With Axial Ribs 668
        
        9.4.10 Beams Loaded With Body and Surface Forces 675
        
        9.4.11 Restrained Torsion and Bending of Beams With Closed Cross-Sectional Contours 676
      - 9.5 Beams With Multicell Cross-Sectional Contours 683
      - 9.6 Beams With Open Cross-Sectional Contours 688
        
        9.6.1 Transverse Bending 688
        
        9.6.2 Free Torsion of Beams With Open Cross-Sectional Contours 693
        
        9.6.3 Restrained Torsion of Beams With Open Cross-Sectional Contours 707
      - References 713
    - 10 Circular Cylindrical Shells 715
      - 10.1 Governing Equations and Applied Shell Theories 715
      - 10.2 Cylindrical Shells Whose Stress–Strain State Does Not Depend on the Axial Coordinate 721
        
        10.2.1 Circular Rings 721
        
        10.2.2 Infinitely Long Cylindrical Panel 727
      - 10.3 Axisymmetric Deformation of Cylindrical Shells 731
        
        10.3.3 Nonlinear Classical Theory 735
        
        10.3.1 Linear Theory of Shear Deformable Shells 735
        
        10.3.4 Nonlinear Membrane Theory 735
        
        10.3.2 Linear Classical Shell Theory 735
        
        10.3.5 Examples 736
        
        10.3.6 Anisotropic Shells 741
      - 10.4 General Loading Case 742
        
        10.4.1 Classical Shell Theory 742
        
        10.4.2 Engineering Shell Theory 745
        
        10.4.3 Semimembrane Shell Theory 745
        
        10.4.4 Membrane Shell Theory 749
        
        10.4.5 Shear Deformable Shell Theory 750
      - 10.5 Buckling of Cylindrical Shells Under Axial Compression 752
        
        10.5.1 Column-Type Buckling 753
        
        10.5.2 Axisymmetric Buckling Mode 753
        
        10.5.3 Nonsymmetric Buckling Mode 759
      - 10.6 Buckling of Cylindrical Shells Under External Pressure 764
        
        10.6.1 Simply Supported Shells 765
        
        10.6.2 Infinitely Long Shells 766
        
        10.6.3 Hydrostatic Pressure 767
      - 10.7 Anisogrid Composite Lattice Cylindrical Shells 768
        
        10.7.1 Fabrication and Applications of Anisogrid Cylindrical Shells 769
        
        10.7.2 Analysis 774
        
        10.7.3 Design 779
      - References 785
    - 11 Shells of Revolution 789
      - 11.1 Basic Equations 789
      - 11.2 Governing Equations of the Linear Theory 792
      - 11.3 Linear Membrane Theory 796
      - 11.4 Linear Boundary-Layer Theory 799
      - 11.5 Nonlinear Theory 804
        
        11.5.1 General Equations 806
        
        11.5.2 Nonlinear Boundary-Layer Theory 807
        
        11.5.3 Nonlinear Membrane Boundary-Layer Theory 809
      - 11.6 Comparison of Boundary-Layer Theories 810
      - References 813
    - 12 Composite Pressure Vessels 815
      - 12.1 Basic Equations 815
      - 12.2 Shells Wound by Unidirectional Composite Tapes 821
        
        12.2.1 Shells Consisting of ±φ Symmetric Monotropic Layers 821
        
        12.2.2 Shells Consisting of a System of ±φi(r) Layers 828
        
        12.2.3 Cylindrical Pressure Vessels 837
      - 12.3 Vessels Formed of Orthotropic Composite Tapes 842
      - References 849
    - Author Index 851
    - Subject Index 857
    - Back Cover 885

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Afiljacja autora

Valery V. Vasiliev: Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia
Evgeny V. Morozov: School of Mechanical Engineering, University of Natal, Durban, South Africa

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