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

by Reddy; J. N.

• ISBN13: 9780849315923
• ISBN10: 0849315921
• Edition: 2nd
• Format: Hardcover
• Copyright: 2003-11-24
• Publisher: CRC Press

Summary

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.

Table of Contents

Preface to the Second Edition	xix
Preface to the First Edition	xxi
1 Equations of Anisotropic Elasticity, Virtual Work Principles, and Variational Methods	1	(80)
1.1 Fiber-Reinforces Composite Materials	1	(2)
1.2 Mathematical Preliminaries	3	(9)
1.2.1 General comments	3	(1)
1.2.2 Vectors and Tensors	3	(9)
1.3 Equations of Anisotropic Entropy	12	(26)
1.3.1 Introduction	12	(1)
1.3.2 Strain-Displacement Equations	13	(5)
1.3.3 Strain compatibility Equations	18	(1)
1.3.4 Stress Measures	18	(1)
1.3.5 Equations of Motion	19	(3)
1.3.6 Generalized Hooke's Law	22	(12)
1.3.7 Thremodynamic Principles	34	(4)
1.4 Virtual Work Principles	38	(20)
1.4.1 Introduction	38	(1)
1.4.2 Virtual Displacements and Virtual Work	38	(2)
1.4.3 Variational Operator and Eater Equations	40	(4)
1.4.4 Principle of Virtual Displacements	44	(14)
1.5 Variational Methods	58	(13)
1.5.1 Introduction	58	(1)
1.5.2 The Ritz Method	58	(6)
1.5.3 Weighted-Residual Methods	64	(7)
1.6 Summary	71	(1)
Problems	72	(6)
References for Additional Reading	78	(3)
2 Introduction to Composite Materials	81	(28)
2.1 Basic Concepts and Terminology	81	(4)
2.1.1 Fibers and Matrix	81	(2)
2.1.2 Laminae and Laminates	83	(2)
2.2 Constitutive Equations of a Lamina	85	(4)
2.2.1 Generalized Hooke's Law	85	(1)
2.2.2 Characteristics of a Unidirectional Lamina	86	(3)
2.3 Transformation of Stresses and Strains	89	(10)
2.3.1 Coordinate Transformations	89	(1)
2.3.2 Transformation of Stress Components	90	(3)
2.3.3 Transformation of Strain Components	93	(3)
2.3.4 Transformation of Material Coefficients	96	(3)
2.4 Plan Stress Constitutive Relations	99	(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