Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, Second Edition

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ISBN: 9780849315923 | 0849315921
Cover: Hardcover
Copyright: 11/24/2003

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The use of composite materials in engineering structures continues to increase dramatically, and in the seven years since the first edition of this book appeared, advances in materials modeling in general and composite materials and structures in particular have been just as significant. To reflect these developments, renowned author, educator, and researcher J.N. Reddy has thoroughly revised, updated, and enhanced his standard-setting Mechanics of Laminated Composite Plates and Shells: Theory and Analysis.New in the Second Edition:· A new chapter dedicated to the theory and analysis of laminated shells· New discussions addressing smart structures and functionally graded materials· Thorough updates to all chapters and a reorganization of chapters that improves the clarity of the presentation· Additional exercises and examplesNo other book is as up to date. No other book approaches the subject primarily from the finite element method. And no other book provides such full, self-contained coverage of the theories, analytical solutions, and linear and nonlinear finite element models of plate and shell laminated composite structures.

Preface to the Second Edition

xix

Preface to the First Edition

xxi

1 Equations of Anisotropic Elasticity, Virtual Work Principles, and Variational Methods

(80)

1.1 Fiber-Reinforces Composite Materials

(2)

1.2 Mathematical Preliminaries

(9)

1.2.1 General comments

(1)

1.2.2 Vectors and Tensors

(9)

1.3 Equations of Anisotropic Entropy

(26)

1.3.1 Introduction

(1)

1.3.2 Strain-Displacement Equations

(5)

1.3.3 Strain compatibility Equations

(1)

1.3.4 Stress Measures

(1)

1.3.5 Equations of Motion

(3)

1.3.6 Generalized Hooke's Law

(12)

1.3.7 Thremodynamic Principles

(4)

1.4 Virtual Work Principles

(20)

1.4.1 Introduction

(1)

1.4.2 Virtual Displacements and Virtual Work

(2)

1.4.3 Variational Operator and Eater Equations

(4)

1.4.4 Principle of Virtual Displacements

(14)

1.5 Variational Methods

(13)

1.5.1 Introduction

(1)

1.5.2 The Ritz Method

(6)

1.5.3 Weighted-Residual Methods

(7)

1.6 Summary

(1)

Problems

(6)

References for Additional Reading

(3)

2 Introduction to Composite Materials

(28)

2.1 Basic Concepts and Terminology

(4)

2.1.1 Fibers and Matrix

(2)

2.1.2 Laminae and Laminates

(2)

2.2 Constitutive Equations of a Lamina

(4)

2.2.1 Generalized Hooke's Law

(1)

2.2.2 Characteristics of a Unidirectional Lamina

(3)

2.3 Transformation of Stresses and Strains

(10)

2.3.1 Coordinate Transformations

(1)

2.3.2 Transformation of Stress Components

(3)

2.3.3 Transformation of Strain Components

(3)

2.3.4 Transformation of Material Coefficients

(3)

2.4 Plan Stress Constitutive Relations

(4)

Problems

103

(3)

References for Additional Reading

106

(3)

3 Classical and First-Order Theories of Laminated Composite Plates

109

(56)

3.1 Introduction

109

(1)

3.1.1 Preliminary Comments

109

(1)

3.1.2 Classification of Structural Theories

109

(1)

3.2 An Overview of Laminated Plate Theories

110

(2)

3.3 The Classical Laminated Plate Theory

112

(20)

3.3.1 Assumptions

112

(1)

3.3.2 Displacements and Strains

113

(4)

3.3.3 Lamina Constitutive Relations

117

(2)

3.3.4 Equations of Motion

119

(8)

3.3.5 Laminate Constitutive Equations

127

(2)

3.3.6 Equations of Motion in Terms of Displacements

129

(3)

3.4 The First-Order Laminated Plate Theory

132

(10)

3.4.1 Displacements and Strains

132

(2)

3.4.2 Equations of Motion

134

(3)

3.4.3 Laminate Constitutive Equations

137

(2)

3.4.4 Equations of Motion in Terms of Displacements

139

(3)

3.5 Laminate Stiffnesses for Selected Laminates

142

(15)

3.5.1 General Discussion

142

(2)

3.5.2 Single-Layer Plates

144

(4)

3.5.3 Symmetric Laminates

148

(4)

3.5.4 Antisymmetris Laminates

152

(4)

3.5.5 Balanced and Quasi-Isotropic Laminates

156

(1)

Problems

157

(4)

References for Additional Reading

161

(4)

4 One-Dimensional Analysis of Laminated Composite Plates

165

(80)

4.1 Introduction

165

(2)

4.2 Analysis of Laminated Beams Using CLPT

167

(20)

4.2.1 Governing Equations

167

(2)

4.2.2 Bending

169

(7)

4.2.3 Buckling

176

(6)

4.2.4 Vibration

182

(5)

4.3 Analysis of Laminated Beams Using FSDT

187

(13)

4.3.1 Governing Equations

187

(1)

4.3.2 Bending

188

(4)

4.3.3 Buckling

192

(5)

4.3.4 Vibration

197

(3)

4.4 Cylindrical Bending Using CLPT

200

(14)

4.4.1 Governing Equations

200

(3)

4.4.2 Bending

203

(5)

4.4.3 Buckling

208

(1)

4.4.4 Vibration

209

(5)

4.5 Cylindrical Bending Using FSDT

214

(8)

4.5.1 Governing Equations

214

(1)

4.5.2 Bending

215

(1)

4.5.3 Buckling

216

(3)

4.5.4 Vibration

219

(3)

4.6 Vibration Suppression in Beams

222

(10)

4.6.1 Introduction

222

(1)

4.6.2 Theoretical Formulation

222

(5)

4.6.3 Analytical Solution

227

(3)

4.6.4 Numerical Results

230

(2)

4.7 Closing Remarks

232

(1)

Problems

232

(10)

References for Additional Reading

242

(3)

5 Analysis of Specially Orthotropic Laminates Using CLPT

245

(52)

5.1 Introduction

245

(1)

5.2 Bending of Simply Supported Rectangular Plates

246

(9)

5.2.1 Governing Equations

246

(1)

5.2.2 The Navier Solution

247

(8)

5.3 Bending of Plates with Two Opposite Edges Simply Supported

255

(10)

5.3.1 The Lévy Solution Procedure

255

(2)

5.3.2 Analytical Solutions

257

(5)

5.3.3 Ritz Solution

262

(3)

5.4 Bending of Rectangular Plates with Various Boundary Conditions

265

(6)

5.4.1 Virtual Work Statements

265

(1)

5.4.2 Clamped Plates

266

(3)

5.4.3 Approximation Functions for Other Boundary Conditions

269

(2)

5.5 Buckling of Simply Supported Plates Under Compressive Loads

271

(7)

5.5.1 Governing Equations

271

(1)

5.5.2 The Navier Solution

272

(1)

5.5.3 Biaxial Compression of a Square Laminate (k = 1)

273

(1)

5.5.4 Biaxial Loading of a Square Laminate

274

(1)

5.5.5 Uniaxial Compression of a Rectangular Laminate (k = 0)

274

(4)

5.6 Buckling of Rectangular Plates Under In-Plane Shear Load

278

(4)

5.6.1 Governing Equation

278

(1)

5.6.2 Simply Supported Plates

278

(2)

5.6.3 Clamped Plates

280

(2)

5.7 Vibration of Simply Supported Plates

282

(3)

5.7.1 Governing Equations

282

(1)

5.7.2 Solution

282

(3)

5.8 Buckling and Vibration of Plates with Two Parallel Edges Simply Supported

285

(5)

5.8.1 Introduction

5.8.2 Buckling by Direct Integration

287

(1)

5.8.3 Vibration by Direct Integration

288

(1)

5.8.4 Buckling and Vibration by the State-Space Approach

288

(2)

5.9 Transient Analysis

290

(3)

5.9.1 Preliminary Comments

290

(1)

5.9.2 Spatial Variation of the Solution

290

(2)

5.9.3 Time Integration

292

(1)

5.10 Closure

293

(1)

Problems

293

(3)

References for Additional Reading

296

(1)

6 Analytical Solutions of Rectangular Laminated Plates Using CLPT

297

(80)

6.1 Governing Equations in Terms of Displacements

297

(2)

6.2 Admissible Boundary Conditions for the Navier Solutions

299

(2)

6.3 Navier Solutions of Cross-Ply Laminates Antisymmetric

301

(527)

6.3.1 Boundary Conditions

301

(3)

6.3.2 Solution

304

(4)

6.3.3 Bending

308

(1)

6.3.4 Determination of Stresses

309

(8)

6.3.5 Buckling

317

(6)

6.3.6 Vibration

323

(505)

6.4 Navier Solutions of Antisymmetric Angle-Ply Laminates

828

6.4.1 Boundary Conditions

326

(2)

6.4.2 Solution

328

(1)

6.4.3 Bending

329

(1)

6.4.4 Determination of Stresses

330

(5)

6.4.5 Buckling

335

(2)

6.4.6 Vibration

337

(2)

6.5 The Lévy Solutions

339

(17)

6.5.1 Introduction

339

(3)

6.5.2 Solution Procedure

342

(6)

8.5.3 Antisymmetric Cross-Ply Laminates

348

(5)

6.5.4 Antisymmetric Angle-Ply Laminates

353

(3)

6.6 Analysis of Midplane Symmetric Laminates

356

(5)

6.6.1 Introduction

356

(1)

6.6.2 Governing Equations

356

(1)

6.6.3 Weak Forms

357

(1)

6.6.4 The Ritz Solution

358

(1)

6.6.5 Simply Supported Plates

358

(2)

6.6.6 Other Boundary Conditions

360

(1)

6.7 Transient Analysis

361

(10)

6.7.1 Preliminary Comments

361

(1)

6.7.2 Equations of Motion

361

(21)

6.7.3 Numerical Time Integration

382

6.7.4 Numerical Results

364

(7)

6.8 Summary

371

(1)

Problems

371

(4)

References for Additional Reading

375

(2)

7 Analytical Solutions of Rectangular Laminated Plates Using FSDT

377

(72)

7.1 Introduction

377

(2)

7.2 Simply Supported Antisymmetric Cross-Ply Laminated Plates

379

(21)

7.2.1 Solution for the General Case

379

(2)

7.2.2 Bending

381

(7)

7.2.3 Buckling

388

(6)

7.2.4 Vibration

394

(6)

7.3 Simply Supported Antisymmetric Angle-Ply Laminated Plates

400

(12)

7.3.1 Boundary Conditions

400

(2)

7.3.2 The Navier Solution

402

(2)

7.3.3 Bending

404

(1)

7.3.4 Buckling

405

(1)

7.3.5 Vibration

406

(6)

7.4 Antisymmetric Cross-Ply Laminates with Two Opposite Edges

412

(9)

7.4.1 Introduction

412

(1)

7.4.2 The Lévy Type Solution

413

(2)

7.4.3 Numerical Examples

415

(6)

7.5 Antisymmetric Angle-Ply Laminates with Two Opposite Edges Simply Supported

421

(9)

7.5.1 Introduction

421

(1)

7.5.2 Governing Equations

421

(2)

7.5.3 The Lévy Solution

423

(2)

7.5.4 Numerical Examples

425

(5)

7.6 Transient Solutions

430

(7)

7.7 Vibration Control of Laminated Plates

437

(5)

7.7.1 Preliminary Comments

437

(1)

7.7.2 Theoretical Formulation

438

(1)

7.7.3 Velocity Feedback Control

438

(1)

7.7.4 Analytical Solution

439

(2)

7.7.5 Numerical Results and Discussion

441

(1)

7.8 Summary

442

(2)

Problems

444

(1)

References for Additional Reading

445

(4)

8 Theory and Analysis of Laminated Shells

449

(38)

8.1 Introduction

449

(1)

8.2 Governing Equations

450

(12)

8.2.1 Geometric Properties of the Shell

450

(4)

8.2.2 Kinetics of the Shell

454

(1)

8.2.3 Kinematic of the Shell

455

(2)

8.2.4 Equations of Motion

457

(4)

8.2.5 Laminate Constitutive Relations

461

(1)

8.3 Theory of Doubly-Curved Shells

462

(11)

8.3.1 Equations of Motion

462

(1)

8.3.2 Analytical Solution

463

(10)

8.4 Vibration and Buckling of Cross-Ply Laminated Circular Cylindrical Shells

473

(10)

8.4.1 Equations of Motion

473

(2)

8.4.2 Analytical Solution Procedure

475

(4)

8.4.3 Boundary Conditions

479

(1)

8.4.4 Numerical Results

480

(3)

Problems

483

(1)

References for Additional

483

(4)

9 Linear Finite Element Analysis of Composite Plates and Shells

487

(80)

9.1 Introduction

487

(1)

9.2 Finite Element Models of the Classical Plate (CLPT) Theory

488

(27)

9.2.1 Weak Forms

488

(2)

9.2.2 Spatial Approximations

490

(9)

9.2.3 Semidiscrete Finite Element Model

499

(1)

9.2.4 Fully Discretized Finite Element Models

500

(3)

9.2.5 Quadrilateral Elements and Numerical Integration

503

(7)

9.2.6 Post-Computation of Stresses

510

(1)

9.2.7 Numerical Results

510

(5)

9.3 Finite Element Models of Shear Deformation Plate (FSDT) Theory

515

(28)

9.3.1 Weak Forms

515

(1)

9.3.2 Finite Element Model

516

(8)

9.3.3 Penalty Function Formulation and Shear Locking 52O

9.3.4 Post-Computation of Stresses

524

(1)

9.3.5 Bending Analysis

525

(17)

9.3.6 Vibration Analysis 54O

9.3.7 Transient Analysis

542

(1)

9.4 Finite Element Analysis of Shells

543

(15)

9.4.1 Weak Forms

543

(3)

9.4.2 Finite Element Model

546

(3)

9.4.3 Numerical Results

549

(9)

9.5 Summary

558

(2)

Problems

560

(1)

References for Additional Reading

560

(7)

10 Nonlinear Analysis of Composite Plates and Shells

567

(104)

10.1 Introduction

567

(1)

10.2 Classical Plate Theory

568

(7)

10.2.1 Governing Equations

568

(1)

10.2.2 Virtual Work Statement

569

(3)

10.2.3 Finite Element Model

572

(3)

10.3 First-Order Shear Deformation Plate Theory

575

(8)

10.3.1 Governing Equations

575

(1)

10.3.2 Virtual Work Statements

576

(2)

10.3.3 Finite Element Model

578

(5)

10.4 Time Approximation and the Newton-Raphson Method

583

(13)

10.4.1 Time Approximations

583

(1)

10.4.2 The Newton-Raphson Method

584

(2)

10.4.3 Tangent Stiffness Coefficients for CLPT

586

(4)

10.4.4 Tangent Stiffness Coefficients for FSDT

590

(4)

10.4.5 Membrane Locking

594

(2)

10.5 Numerical Examples of Plates

596

(17)

10.5.1 Preliminary Comments

596

(1)

10.5.2 Isotropic and Orthotropic Plates

596

(5)

10.5.3 Laminated Composite Plates

601

(3)

10.5.4 Effect of Symmetry Boundary Conditions on Nonlinear Response

604

(4)

10.5.5 Nonlinear Response Under In-Plane Compressive Loads

608

(1)

10.5.6 Nonlinear Response of Antisymmetric Cross-Ply Laminated Plate Strips

608

(4)

10.5.7 Transient Analysis of Composite Plates

612

(1)

10.6 Functionally Graded Plates

613

(8)

10.6.1 Background

613

(2)

10.6.2 Theoretical Formulation

615

(1)

10.6.3 Thermomechanical Coupling

616

(1)

10.6.4 Numerical Results

617

(4)

10.7 Finite Element Models of Laminated Shell Theory

621

(6)

10.7.1 Governing Equations

621

(1)

10.7.2 Finite Element Model

622

(3)

10.7.3 Numerical Examples

625

(2)

10.8 Continuum Shell Finite Element

627

(218)

10.8.1 Introduction

627

(1)

10.8.2 Incremental of Motion Equations

628

(3)

10.8.3 Continuum Finite Element Model

631

(2)

10.8.4 Shell Finite Element

633

(5)

10.8.5 Numerical Examples

638

(6)

10.8.6 Closure

644

(201)

10.9 Postbuckling Response and Progressive Failure of Composite Panels in Compression

845

10.9.1 Preliminary Comments

645

(1)

10.9.2 Experimental Study

645

(2)

10.9.3 Finite Element Models

647

(1)

10.9.4 Failure Analysis

648

(2)

10.9.5 Results for Panel C4

650

(8)

10.9.6 Results for Panel H4

658

(1)

10.10 Closure

658

(1)

Problems

658

(6)

References for Additional Reading

664

(7)

11 Third-Order Theory of Laminated Composite Plates and Shells

671

(54)

11.1 Introduction

671

(1)

11.2 A Third-Order Plate Theory

671

(6)

11.2.1 Displacement Field

671

(3)

11.2.2 Strains and Stresses

674

(1)

11.2.3 Equations of Motion

674

(3)

11.3 Higher-Order Laminate Stiffness Characteristics

677

(5)

11.3.1 Single-Layer Plates

678

(2)

11.3.2 Symmetric Laminates

680

(1)

11.3.3 Antisymmetric Laminates

681

(1)

11.4 The Navier Solutions

682

(17)

11.4.1 Preliminary Comments

682

(2)

11.4.2 Antisymmetric Cross-Ply Laminates

684

(3)

11.4.3 Antisymmetric Angle-Ply Laminates

687

(2)

11.4.4 Numerical Results

689

(10)

11.5 Lévy Solutions of Cross-Ply Laminates

699

(7)

11.5.1 Preliminary Comments

699

(2)

11.5.2 Solution Procedure

701

(3)

11.5.3 Numerical Results

704

(2)

11.6 Finite Element Model of Plates

706

(12)

11.6.1 Introduction

706

(1)

11.6.2 Finite Element Model

707

(5)

11.6.3 Numerical Results

712

(2)

11.6.4 Closure

714

(4)

11.7 Equations of Motion of the Third-Order Theory of Doubly-Curved Shells

718

(2)

Problems

720

(1)

References for Additional Reading

721

(4)

12 Layerwise Theory and Variable Kinematic Models

725

(96)

12.1 Introduction

725

(5)

12.1.1 Motivation

725

(1)

12.1.2 An Overview of Layerwise Theories

726

(4)

12.2 Development of the Theory

730

(8)

12.2.1 Displacement Field

730

(3)

12.2.2 Strains and Stresses

733

(1)

12.2.3 Equations of Motion

734

(2)

12.2.4 Laminate Constitutive Equations

736

(2)

12.3 Finite Element Model

738

(21)

12.3.1 Layerwise Model

738

(1)

12.3.2 Full Layerwise Model Versus 3-D Finite Element Model

739

(3)

12.3.3 Considerations for Modeling Relatively Thin Laminates

742

(4)

12.3.4 Bending of a Simply Supported (0/90/0) Laminate

746

(7)

12.3.5 Free Edge Stresses in a (45/-45)s Laminate

753

(6)

12.4 Variable Kinematic Formulations

759

(21)

12.4.1 Introduction

759

(3)

12.4.2 Multiple Assumed Displacement Fields

762

(2)

12.4.3 Incorporation of Delamination Kinematics

764

(2)

12.4.4 Finite Element Model

766

(3)

12.4.5 Illustrative Examples

769

(11)

12.5 Application to Adaptive Structures

780

(14)

12.5.1 Introduction

780

(3)

12.5.2 Governing Equations

783

(2)

12.5.3 Finite Element Model

785

(2)

12.5.4 An Example

787

(7)

12.6 Layerwise Theory of Cylindrical Shells

794

(18)

12.6.1 Introduction

794

(1)

12.6.2 Unstiffened Shells

794

(4)

12.6.3 Stiffened Shells

798

(8)

12.6.4 Postbuckling of Laminated Cylinders

806

(6)

12.7 Closure

812

(4)

References for Additional Reading

816

(5)

Subject Index

821

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Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, Second Edition

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