Practical Analysis of Composite Laminates (Applied and Computational Mechanics)

Composite materials are increasingly used in aerospace, underwater, and automotive structures. They provide unique advantages over their metallic counterparts, but also create complex challenges to analysts and designers. Practical Analysis of Composite Laminates presents a summary of the equations governing composite laminates and provides practical methods for analyzing most common types of composite structural elements. Experimental results for several types of structures are included, and theoretical and experimental correlations are discussed. The last chapter is devoted to practical analysis using Designing Advanced Composites (DAC), a PC-based software on the subject. This comprehensive text can be used for a graduate course in mechanical engineering, and as a valuable reference for professionals in the field. Cover 1 Title Page 4 Copyright Page 5 PREFACE 6 ABOUT THE AUTHORS 8 Dedication 10 Table of Contents 12 Half Title 16 1: INTRODUCTION AND PRELIMINARIES 17 1.1 Introduction 17 1.2 Present Study 18 1.3 Mathematical Preliminaries 18 Exercise Problems 25 References for Additional Reading 26 2: REVIEW OF GOVERNING EQUATIONS 27 2.1 Classification of Equations 27 2.2 Kinematics 28 2.3 Kinetics 31 2.3–1 Stress 31 2.3–2 Equations of Motion 33 2.4 Constitutive Equations 35 2.5 Summary 37 Exercise Problems 38 References for Additional Reading 40 3: MECHANICAL BEHAVIOR OF COMPOSITE MATERIALS 41 3.1 Terminology and Definitions 41 3.2 Lamina Constitutive Equations 44 3.2–1 Generalized Hooke’s Law 44 3.2–2 Engineering Constants of Orthotropic Materials 48 3.2–3 Characterization of a Unidirectional Lamina 50 3.3 Transformation of Stresses and Strains 53 3.3–1 Coordinate Transformations 12 3.3–2 Transformation of Stress Components 54 3.3–3 Transformation of Strain Components 56 3.3–4 Transformation of Elastic Coefficients 58 3.4 Constitutive Relations for Plane Stress 59 Exercise Problems 64 References for Additional Reading 64 4: THEORIES OF LAMINATED PLATES 67 4.1 Introduction 67 4.2 Classical Laminated Plate Theory 68 4.2–1 Introduction 68 4.2–2 Displacements and Strains 68 4.2–3 Equations of Motion 71 4.2–4 Laminate Constitutive Equations 74 4.2–5 Equations of Motion in Terms of Displacements 76 4.3 The First-Order Shear Deformation Theory 77 4.3- 1 Displacement Field and Strai 77 4.3- 2 Equations of Motion 79 4.4 Stiffness Characteristics of Selected Lamination Schemes 82 4.4–1 Terminology and Notation 82 4.4–2 Single–Layer, Generally Orthotropic, Plates 83 4.4–3 Symmetric Laminates 84 4.4–4 Antisymmetric Laminates 86 Exercise Problems 64 References For Additional Reading 95 5: ANALYSIS OF RECTANGULAR PLATES 97 5.1 Introduction 97 5.2 The Navier Solutions 98 5.2–1 Boundary Conditions 98 5.2–2 General Solution 99 5.2–3 Bending Analysis 101 5.2–4 Buckling Analysis 102 5.2–5 Vibration Analysis 105 5.3 The Levy Solution 108 5.3–1 Introduction 108 5.3–2 Operator Form of Governing Equations 108 5.3–3 Solution Procedure 110 5.4 Finite Element Models 115 5.4–1 Classical Laminated Plate Theory 115 5.4–2 First–Order Shear Deformation Theory 121 5.4–3 Bending, Stability, and Vibration Models 125 5.4–4 Transient Analysis 127 5.4–5 Shear locking 130 5.5 Computation of Stresses and Strains 131 5.6 Example Problems 133 5.6–1 General Comments 133 5.6–2 Bending Analysis 134 5.6–3 Vibration and Buckling Analyses 145 References for Additional Reading 151 6: FAILURES IN COMPOSITE LAMINATES 157 6.1 Introduction 157 6.2 Matrix Cracks 158 6.2–1 Shear Lag Models 158 6.2–2 Variational Models 162 6.2–3 Continuum Damage Models 163 6.2–4 Elasticity Models 164 6.2–5 Self-Consistent Model and Other Models 164 6.3 Delaminations 165 6.4 Fiber Pull/Push Out 167 6.5 Failure Criteria 169 6.5–1 General Comments 169 6.5–2 Independent Failure Criteria 170 6.5–3 Polynomial Failure Criteria 171 References for Additional Reading 177 7: VARIABLE THICKNESS STRUCTURES 187 7.1 Introduction 187 7.2 Theoretical Background 188 7.3 The Effect of Stress Concentration 191 7.3–1 Introduction 191 7.3–2 Stress Distributions 192 7.3–3 Failure Mechanisms 198 7.4 Examples 201 7.4–1 Preliminary Comments 201 7.4–2 Model Assumptions and Method of Analysis 201 7.4–3 Laminated Composite Beams 203 7.4–4 Laminated Composite Plates 206 7.5 Correlation of Theory and Experiment 212 References for Additional Reading 224 8: CRASH ANALYSIS 227 8.1 Introduction 227 8.2 Theoretical Formulation 228 8.2–1 Introduction 228 8.2–2 Descriptions of Motion 229 8.2–3 Governing Equations 230 8.2–4 Spatial Finite Element Discretization 232 8.2–5 Computational Aspects 235 8.3 Correlation of Theory and Experiment 239 8.3–1 Pultruded Tubes 240 8.3–2 The 3-D Fabrics 244 8.3–3 Car Front Energy Absorber (Bumper) 250 References For Additional Reading 268 9: ANALYSIS OF LARGE STRUCTURES 273 9.1 Introduction 273 9.2 The Substructuring Technique 274 9.3 Analysis Considerations 283 9.3–1 Analysis Aspects 283 9.3–2 Substructuring Work Scheme and Procedure 285 9.4 The Design of a Bus Structure 287 9.4–1 Introduction 15 9.4–2 Analytical Design of a Bus Structure 287 9.4–3 Finite Element Analysis 290 9.4–4 Optimization 293 9.4–5 Conclusions 295 10: PRACTICAL ANALYSIS WITH DAC 299 10.1 Introduction 299 10.1–1 General Comments 299 10.1–2 Why DAC? 300 10.2 DAC SOFTWARE 301 10.2–1 Software and Hardware Requirements 301 10.2–2 Computational Time 301 10.2–3 Accuracy of the Results 303 10.3 DAC Plates/Sandwich Program 306 10.4 DAC Reinforced Sandwiches Program 308 10.5 Sample Applications 312 10.5–1 Advertisement Sign Board 312 10.5–2 Trailer Floor 321 10.6 Closure 322 References for Additional Reading 327 SUBJECT INDEX 329 Presents a summary of the equations governing composite laminates and offers practical methods for analyzing the common types of composite structural elements. This book features practical analysis using Designing Advanced Composites (DAC), a PC-based software on the subject. It is suitable for graduate courses in mechanical engineering. The book serves as a reference for practicing engineers and designers of composite materials. It can also be used as a text book at the graduate level.