Mechanics of laminated composite plates and shells : theory and analysis / J.N. Reddy.

By: Reddy, J. N. (Junuthula Narasimha), 1945-.

Contributor(s): Reddy, J. N. (Junuthula Narasimha), 1945-. Mechanics of laminated composite plates.

Material type: materialTypeLabel

BookPublisher: Boca Raton : CRC Press, c2004Edition: 2nd ed.Description: xxiii, 831 p. : ill. ; 26 cm. + hbk.ISBN: 0849315921 .Subject(s): Plates (Engineering) -- Mathematical models | Shells (Engineering) -- Mathematical models | Laminated materials -- Mechanical properties -- Mathematical models | Composite materials -- Mechanical properties -- Mathematical modelsDDC classification: 624.17765

Contents:

Equations of anistropic elasticity, virtual work principles, and variational methods -- Introduction to composite materials -- Classical and first-order theories of laminated composite plates -- One-dimensional analysis of laminated composite plates -- Analysis of specially orthotropic laminates using CLPT -- Analytical solutions of rectangular laminated plates using CLPT -- Analytical solutions of rectangular laminated plates using FSDT -- Theory and analysis of laminated shells -- Linear finite element analysis of composite plates and shells -- Nonlinear analysis of composite plates and shells -- Third-order theory of laminated composite plates and shells -- Layerwise theory and variable kinematic models.

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Enhanced descriptions from Syndetics:

The use of composite materials in engineering structures continues to increase dramatically, and there have been equally significant advances in modeling for general and composite materials and structures in particular. To reflect these developments, renowned author, educator, and researcher J.N. Reddy created an enhanced second edition of his standard-setting Mechanics of Laminated Composite Plates and Shells: Theory and Analysis.

This edition includes:

A chapter dedicated to the theory and analysis of laminated shells
Discussions addressing smart structures and functionally graded materials
Reorganization of chapters that improves and clarifies presentation
Additional exercises and examples

A timelessly valuable resource, this book approaches the subject primarily in terms of the finite element method. It provides incomparably full, self-contained coverage of the theories, analytical solutions, and linear and nonlinear finite element models of plate and shell laminated composite structures.

Rev. ed. of: Mechanics of laminated composite plates. c1997.

Includes bibliographical references and index.

Table of contents provided by Syndetics

Preface to the Second Edition (p. xix)
Preface to the First Edition (p. xxi)
1 Equations of Anisotropic Elasticity, Virtual Work Principles, and Variational Methods (p. 1)
1.1 Fiber-Reinforced Composite Materials (p. 1)
1.2 Mathematical Preliminaries (p. 3)
1.2.1 General Comments (p. 3)
1.2.2 Vectors and Tensors (p. 3)
1.3 Equations of Anisotropic Entropy (p. 12)
1.3.1 Introduction (p. 12)
1.3.2 Strain-Displacement Equations (p. 13)
1.3.3 Strain Compatibility Equations (p. 18)
1.3.4 Stress Measures (p. 18)
1.3.5 Equations of Motion (p. 19)
1.3.6 Generalized Hooke's Law (p. 22)
1.3.7 Thermodynamic Principles (p. 34)
1.4 Virtual Work Principles (p. 38)
1.4.1 Introduction (p. 38)
1.4.2 Virtual Displacements and Virtual Work (p. 38)
1.4.3 Variational Operator and Euler Equations (p. 40)
1.4.4 Principle of Virtual Displacements (p. 44)
1.5 Variational Methods (p. 58)
1.5.1 Introduction (p. 58)
1.5.2 The Ritz Method (p. 58)
1.5.3 Weighted-Residual Methods (p. 64)
1.6 Summary (p. 71)
Problems (p. 72)
References for Additional Reading (p. 78)
2 Introduction to Composite Materials (p. 81)
2.1 Basic Concepts and Terminology (p. 81)
2.1.1 Fibers and Matrix (p. 81)
2.1.2 Laminae and Laminates (p. 83)
2.2 Constitutive Equations of a Lamina (p. 85)
2.2.1 Generalized Hooke's Law (p. 85)
2.2.2 Characteristics of a Unidirectional Lamina (p. 86)
2.3 Transformation of Stresses and Strains (p. 89)
2.3.1 Coordinate Transformations (p. 89)
2.3.2 Transformation of Stress Components (p. 90)
2.3.3 Transformation of Strain Components (p. 93)
2.3.4 Transformation of Material Coefficients (p. 96)
2.4 Plan Stress Constitutive Relations (p. 99)
Problems (p. 103)
References for Additional Reading (p. 106)
3 Classical and First-Order Theories of Laminated Composite Plates (p. 109)
3.1 Introduction (p. 109)
3.1.1 Preliminary Comments (p. 109)
3.1.2 Classification of Structural Theories (p. 109)
3.2 An Overview of Laminated Plate Theories (p. 110)
3.3 The Classical Laminated Plate Theory (p. 112)
3.3.1 Assumptions (p. 112)
3.3.2 Displacements and Strains (p. 113)
3.3.3 Lamina Constitutive Relations (p. 117)
3.3.4 Equations of Motion (p. 119)
3.3.5 Laminate Constitutive Equations (p. 127)
3.3.6 Equations of Motion in Terms of Displacements (p. 129)
3.4 The First-Order Laminated Plate Theory (p. 132)
3.4.1 Displacements and Strains (p. 132)
3.4.2 Equations of Motion (p. 134)
3.4.3 Laminate Constitutive Equations (p. 137)
3.4.4 Equations of Motion in Terms of Displacements (p. 139)
3.5 Laminate Stiffnesses for Selected Laminates (p. 142)
3.5.1 General Discussion (p. 142)
3.5.2 Single-Layer Plates (p. 144)
3.5.3 Symmetric Laminates (p. 148)
3.5.4 Antisymmetric Laminates (p. 152)
3.5.5 Balanced and Quasi-Isotropic Laminates (p. 156)
Problems (p. 157)
References for Additional Reading (p. 161)
4 One-Dimensional Analysis of Laminated Composite Plates (p. 165)
4.1 Introduction (p. 165)
4.2 Analysis of Laminated Beams Using CLPT (p. 167)
4.2.1 Governing Equations (p. 167)
4.2.2 Bending (p. 169)
4.2.3 Buckling (p. 176)
4.2.4 Vibration (p. 182)
4.3 Analysis of Laminated Beams Using FSDT (p. 187)
4.3.1 Governing Equations (p. 187)
4.3.2 Bending (p. 188)
4.3.3 Buckling (p. 192)
4.3.4 Vibration (p. 197)
4.4 Cylindrical Bending Using CLPT (p. 200)
4.4.1 Governing Equations (p. 200)
4.4.2 Bending (p. 203)
4.4.3 Buckling (p. 208)
4.4.4 Vibration (p. 209)
4.5 Cylindrical Bending Using FSDT (p. 214)
4.5.1 Governing Equations (p. 214)
4.5.2 Bending (p. 215)
4.5.3 Buckling (p. 216)
4.5.4 Vibration (p. 219)
4.6 Vibration Suppression in Beams (p. 222)
4.6.1 Introduction (p. 222)
4.6.2 Theoretical Formulation (p. 222)
4.6.3 Analytical Solution (p. 227)
4.6.4 Numerical Results (p. 230)
4.7 Closing Remarks (p. 232)
Problems (p. 232)
References for Additional Reading (p. 242)
5 Analysis of Specially Orthotropic Laminates Using CLPT (p. 245)
5.1 Introduction (p. 245)
5.2 Bending of Simply Supported Rectangular Plates (p. 246)
5.2.1 Governing Equations (p. 246)
5.2.2 The Navier Solution (p. 247)
5.3 Bending of Plates with Two Opposite Edges Simply Supported (p. 255)
5.3.1 The Levy Solution Procedure (p. 255)
5.3.2 Analytical Solutions (p. 257)
5.3.3 Ritz Solution (p. 262)
5.4 Bending of Rectangular Plates with Various Boundary Conditions (p. 265)
5.4.1 Virtual Work Statements (p. 265)
5.4.2 Clamped Plates (p. 266)
5.4.3 Approximation Functions for Other Boundary Conditions (p. 269)
5.5 Buckling of Simply Supported Plates Under Compressive Loads (p. 271)
5.5.1 Governing Equations (p. 271)
5.5.2 The Navier Solution (p. 272)
5.5.3 Biaxial Compression of a Square Laminate (k = 1) (p. 273)
5.5.4 Biaxial Loading of a Square Laminate (p. 274)
5.5.5 Uniaxial Compression of a Rectangular Laminate (k = 0) (p. 274)
5.6 Buckling of Rectangular Plates Under In-Plane Shear Load (p. 278)
5.6.1 Governing Equation (p. 278)
5.6.2 Simply Supported Plates (p. 278)
5.6.3 Clamped Plates (p. 280)
5.7 Vibration of Simply Supported Plates (p. 282)
5.7.1 Governing Equations (p. 282)
5.7.2 Solution (p. 282)
5.8 Buckling and Vibration of Plates with Two Parallel Edges Simply Supported (p. 285)
5.8.1 Introduction (p. 285)
5.8.2 Buckling by Direct Integration (p. 287)
5.8.3 Vibration by Direct Integration (p. 288)
5.8.4 Buckling and Vibration by the State-Space Approach (p. 288)
5.9 Transient Analysis (p. 290)
5.9.1 Preliminary Comments (p. 290)
5.9.2 Spatial Variation of the Solution (p. 290)
5.9.3 Time Integration (p. 292)
5.10 Closure (p. 293)
Problems (p. 293)
References for Additional Reading (p. 296)
6 Analytical Solutions of Rectangular Laminated Plates Using CLPT (p. 297)
6.1 Governing Equations in Terms of Displacements (p. 297)
6.2 Admissible Boundary Conditions for the Navier Solutions (p. 299)
6.3 Navier Solutions of Antisymmetric Cross-Ply Laminates (p. 301)
6.3.1 Boundary Conditions (p. 301)
6.3.2 Solution (p. 304)
6.3.3 Bending (p. 308)
6.3.4 Determination of Stresses (p. 309)
6.3.5 Buckling (p. 317)
6.3.6 Vibration (p. 323)
6.4 Navier Solutions of Antisymmetric Angle-Ply Laminates (p. 326)
6.4.1 Boundary Conditions (p. 326)
6.4.2 Solution (p. 328)
6.4.3 Bending (p. 329)
6.4.4 Determination of Stresses (p. 330)
6.4.5 Buckling (p. 335)
6.4.6 Vibration (p. 337)
6.5 The Levy Solutions (p. 339)
6.5.1 Introduction (p. 339)
6.5.2 Solution Procedure (p. 342)
6.5.3 Antisymmetric Cross-Ply Laminates (p. 348)
6.5.4 Antisymmetric Angle-Ply Laminates (p. 353)
6.6 Analysis of Midplane Symmetric Laminates (p. 356)
6.6.1 Introduction (p. 356)
6.6.2 Governing Equations (p. 356)
6.6.3 Weak Forms (p. 357)
6.6.4 The Ritz Solution (p. 358)
6.6.5 Simply Supported Plates (p. 358)
6.6.6 Other Boundary Conditions (p. 360)
6.7 Transient Analysis (p. 361)
6.7.1 Preliminary Comments (p. 361)
6.7.2 Equations of Motion (p. 361)
6.7.3 Numerical Time Integration (p. 362)
6.7.4 Numerical Results (p. 364)
6.8 Summary (p. 371)
Problems (p. 371)
References for Additional Reading (p. 375)
7 Analytical Solutions of Rectangular Laminated Plates Using FSDT (p. 377)
7.1 Introduction (p. 377)
7.2 Simply Supported Antisymmetric Cross-Ply Laminated Plates (p. 379)
7.2.1 Solution for the General Case (p. 379)
7.2.2 Bending (p. 381)
7.2.3 Buckling (p. 388)
7.2.4 Vibration (p. 394)
7.3 Simply Supported Antisymmetric Angle-Ply Laminated Plates (p. 400)
7.3.1 Boundary Conditions (p. 400)
7.3.2 The Navier Solution (p. 402)
7.3.3 Bending (p. 404)
7.3.4 Buckling (p. 405)
7.3.5 Vibration (p. 406)
7.4 Antisymmetric Cross-Ply Laminates with Two Opposite Edges Simply Supported (p. 412)
7.4.1 Introduction (p. 412)
7.4.2 The Levy Type Solution (p. 413)
7.4.3 Numerical Examples (p. 415)
7.5 Antisymmetric Angle-Ply Laminates with Two Opposite Edges Simply Supported (p. 421)
7.5.1 Introduction (p. 421)
7.5.2 Governing Equations (p. 421)
7.5.3 The Levy Solution (p. 423)
7.5.4 Numerical Examples (p. 425)
7.6 Transient Solutions (p. 430)
7.7 Vibration Control of Laminated Plates (p. 437)
7.7.1 Preliminary Comments (p. 437)
7.7.2 Theoretical Formulation (p. 438)
7.7.3 Velocity Feedback Control (p. 438)
7.7.4 Analytical Solution (p. 439)
7.7.5 Numerical Results and Discussion (p. 441)
7.8 Summary (p. 442)
Problems (p. 444)
References for Additional Reading (p. 445)
8 Theory and Analysis of Laminated Shells (p. 449)
8.1 Introduction (p. 449)
8.2 Governing Equations (p. 450)
8.2.1 Geometric Properties of the Shell (p. 450)
8.2.2 Kinetics of the Shell (p. 454)
8.2.3 Kinematics of the Shell (p. 455)
8.2.4 Equations of Motion (p. 457)
8.2.5 Laminate Constitutive Relations (p. 461)
8.3 Theory of Doubly-Curved Shells (p. 462)
8.3.1 Equations of Motion (p. 462)
8.3.2 Analytical Solution (p. 463)
8.4 Vibration and Buckling of Cross-Ply Laminated Circular Cylindrical Shells (p. 473)
8.4.1 Equations of Motion (p. 473)
8.4.2 Analytical Solution Procedure (p. 475)
8.4.3 Boundary Conditions (p. 479)
8.4.4 Numerical Results (p. 480)
Problems (p. 483)
References for Additional Reading (p. 483)
9 Linear Finite Element Analysis of Composite Plates and Shells (p. 487)
9.1 Introduction (p. 487)
9.2 Finite Element Models of the Classical Plate Theory (CLPT) (p. 488)
9.2.1 Weak Forms (p. 488)
9.2.2 Spatial Approximations (p. 490)
9.2.3 Semidiscrete Finite Element Model (p. 499)
9.2.4 Fully Discretized Finite Element Models (p. 500)
9.2.5 Quadrilateral Elements and Numerical Integration (p. 503)
9.2.6 Post-Computation of Stresses (p. 510)
9.2.7 Numerical Results (p. 510)
9.3 Finite Element Models of Shear Deformation Plate Theory (FSDT) (p. 515)
9.3.1 Weak Forms (p. 515)
9.3.2 Finite Element Model (p. 516)
9.3.3 Penalty Function Formulation and Shear Locking (p. 520)
9.3.4 Post-Computation of Stresses (p. 524)
9.3.5 Bending Analysis (p. 525)
9.3.6 Vibration Analysis (p. 540)
9.3.7 Transient Analysis (p. 542)
9.4 Finite Element Analysis of Shells (p. 543)
9.4.1 Weak Forms (p. 543)
9.4.2 Finite Element Model (p. 546)
9.4.3 Numerical Results (p. 549)
9.5 Summary (p. 558)
Problems (p. 560)
References for Additional Reading (p. 560)
10 Nonlinear Analysis of Composite Plates and Shells (p. 567)
10.1 Introduction (p. 567)
10.2 Classical Plate Theory (p. 568)
10.2.1 Governing Equations (p. 568)
10.2.2 Virtual Work Statement (p. 569)
10.2.3 Finite Element Model (p. 572)
10.3 First-Order Shear Deformation Plate Theory (p. 575)
10.3.1 Governing Equations (p. 575)
10.3.2 Virtual Work Statements (p. 576)
10.3.3 Finite Element Model (p. 578)
10.4 Time Approximation and the Newton-Raphson Method (p. 583)
10.4.1 Time Approximations (p. 583)
10.4.2 The Newton-Raphson Method (p. 584)
10.4.3 Tangent Stiffness Coefficients for CLPT (p. 586)
10.4.4 Tangent Stiffness Coefficients for FSDT (p. 590)
10.4.5 Membrane Locking (p. 594)
10.5 Numerical Examples of Plates (p. 596)
10.5.1 Preliminary Comments (p. 596)
10.5.2 Isotropic and Orthotropic Plates (p. 596)
10.5.3 Laminated Composite Plates (p. 601)
10.5.4 Effect of Symmetry Boundary Conditions on Nonlinear Response (p. 604)
10.5.5 Nonlinear Response Under In-Plane Compressive Loads (p. 608)
10.5.6 Nonlinear Response of Antisymmetric Cross-Ply Laminated Plate Strips (p. 608)
10.5.7 Transient Analysis of Composite Plates (p. 612)
10.6 Functionally Graded Plates (p. 613)
10.6.1 Background (p. 613)
10.6.2 Theoretical Formulation (p. 615)
10.6.3 Thermomechanical Coupling (p. 616)
10.6.4 Numerical Results (p. 617)
10.7 Finite Element Models of Laminated Shell Theory (p. 621)
10.7.1 Governing Equations (p. 621)
10.7.2 Finite Element Model (p. 622)
10.7.3 Numerical Examples (p. 625)
10.8 Continuum Shell Finite Element (p. 627)
10.8.1 Introduction (p. 627)
10.8.2 Incremental Equations of Motion (p. 628)
10.8.3 Continuum Finite Element Model (p. 631)
10.8.4 Shell Finite Element (p. 633)
10.8.5 Numerical Examples (p. 638)
10.8.6 Closure (p. 644)
10.9 Postbuckling Response and Progressive Failure of Composite Panels in Compression (p. 645)
10.9.1 Preliminary Comments (p. 645)
10.9.2 Experimental Study (p. 645)
10.9.3 Finite Element Models (p. 647)
10.9.4 Failure Analysis (p. 648)
10.9.5 Results for Panel C4 (p. 650)
10.9.6 Results for Panel H4 (p. 655)
10.10 Closure (p. 658)
Problems (p. 658)
References for Additional Reading (p. 664)
11 Third-Order Theory of Laminated Composite Plates and Shells (p. 671)
11.1 Introduction (p. 671)
11.2 A Third-Order Plate Theory (p. 671)
11.2.1 Displacement Field (p. 671)
11.2.2 Strains and Stresses (p. 674)
11.2.3 Equations of Motion (p. 674)
11.3 Higher-Order Laminate Stiffness Characteristics (p. 677)
11.3.1 Single-Layer Plates (p. 678)
11.3.2 Symmetric Laminates (p. 680)
11.3.3 Antisymmetric Laminates (p. 681)
11.4 The Navier Solutions (p. 682)
11.4.1 Preliminary Comments (p. 682)
11.4.2 Antisymmetric Cross-Ply Laminates (p. 684)
11.4.3 Antisymmetric Angle-Ply Laminates (p. 687)
11.4.4 Numerical Results (p. 689)
11.5 Levy Solutions of Cross-Ply Laminates (p. 699)
11.5.1 Preliminary Comments (p. 699)
11.5.2 Solution Procedure (p. 701)
11.5.3 Numerical Results (p. 704)
11.6 Finite Element Model of Plates (p. 706)
11.6.1 Introduction (p. 706)
11.6.2 Finite Element Model (p. 707)
11.6.3 Numerical Results (p. 712)
11.6.4 Closure (p. 714)
11.7 Equations of Motion of the Third-Order Theory of Doubly-Curved Shells (p. 718)
Problems (p. 720)
References for Additional Reading (p. 721)
12 Layerwise Theory and Variable Kinematic Models (p. 725)
12.1 Introduction (p. 725)
12.1.1 Motivation (p. 725)
12.1.2 An Overview of Layerwise Theories (p. 726)
12.2 Development of the Theory (p. 730)
12.2.1 Displacement Field (p. 730)
12.2.2 Strains and Stresses (p. 733)
12.2.3 Equations of Motion (p. 734)
12.2.4 Laminate Constitutive Equations (p. 736)
12.3 Finite Element Model (p. 738)
12.3.1 Layerwise Model (p. 738)
12.3.2 Full Layerwise Model Versus 3-D Finite Element Model (p. 739)
12.3.3 Considerations for Modeling Relatively Thin Laminates (p. 742)
12.3.4 Bending of a Simply Supported (0/90/0) Laminate (p. 746)
12.3.5 Free Edge Stresses in a (45/-45)[subscript s] Laminate (p. 753)
12.4 Variable Kinematic Formulations (p. 759)
12.4.1 Introduction (p. 759)
12.4.2 Multiple Assumed Displacement Fields (p. 762)
12.4.3 Incorporation of Delamination Kinematics (p. 764)
12.4.4 Finite Element Model (p. 766)
12.4.5 Illustrative Examples (p. 769)
12.5 Application to Adaptive Structures (p. 780)
12.5.1 Introduction (p. 780)
12.5.2 Governing Equations (p. 783)
12.5.3 Finite Element Model (p. 785)
12.5.4 An Example (p. 787)
12.6 Layerwise Theory of Cylindrical Shells (p. 794)
12.6.1 Introduction (p. 794)
12.6.2 Unstiffened Shells (p. 794)
12.6.3 Stiffened Shells (p. 798)
12.6.4 Postbuckling of Laminated Cylinders (p. 806)
12.7 Closure (p. 812)
References for Additional Reading (p. 816)
Subject Index (p. 821)

Mechanics of laminated composite plates and shells : theory and analysis / J.N. Reddy.

By: Reddy, J. N. (Junuthula Narasimha), 1945-.

Contributor(s): Reddy, J. N. (Junuthula Narasimha), 1945-. Mechanics of laminated composite plates.

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