Mechanics of Laminated Composite Structures

✍ Scribed by Chyanbin Hwu

• Publisher: CRC Press
• Year: 2024
• Tongue: English
• Leaves: 415
• Edition: 1
• Category: Library

✦ Synopsis

In this textbook for students of laminated composite materials, composite structures, and anisotropic elasticity, Chyanbin Hwu draws on more than three decades of research and applications experience to provide a leading resource on many unique topics related to laminated composite structures.

This book introduces the mechanical behavior of laminated composite materials and provides related theories and solutions. All basic structural elements such as beams, plates, and shells are described in detail. Further contents include composite sandwich construction and composite wing structures. To connect with practical engineering applications and analyze more complicated real structures, numerical methods and their theoretical basis in anisotropic elasticity are also included. Advanced topics addressed include solutions for magneto-electro-elastic laminated plates; Green’s functions for thick laminated plates and beams; typical thick laminated beams; theory for general laminated composite shells; sandwich beams, plates, and cylindrical shells as well as delaminated composite sandwich beams; modeling and analysis of composite wing structures; complex variable theories of anisotropic elasticity and the related Green’s functions; and numerical methods such as finite element method, boundary element method and meshless method. Through this book, readers will learn not only the mechanics of laminated composite structures but also anisotropic elasticity and some popular numerical methods.

This textbook is vital for advanced undergraduate and graduate students interested in the mechanics of composite materials, composite structures, and anisotropic elasticity, such as aerospace, mechanical, civil, and naval engineering; applied mechanics; and engineering science. It is also useful for engineers working in these fields and applied mathematicians and material scientists.

✦ Table of Contents

Cover
Endorsement Page
Half Title
Title Page
Copyright Page
Table of Contents
Preface
Chapter 1: Introduction to Composites
1.1 Classification and Characteristics of Composite Materials
1.2 Fabrication of Fiber-Reinforced Composite Materials
1.2.1 Fibers
1.2.2 Matrix
1.2.3 Fabrication
1.3 Mechanical Behavior of Composite Materials
1.4 Composite Structures
Notes
References
Chapter 2: Mechanical Behavior of Laminated Composite Materials
2.1 Lamina Elastic Behavior
2.1.1 Specially Orthotropic Lamina
2.1.2 Generally Orthotropic Lamina
2.2 Micromechanics Prediction of Lamina Stiffness
2.2.1 Mechanics of Materials Approach
2.2.2 Elasticity Approach
2.3 Lamina Strength
2.3.1 Longitudinal Tensile Strength
2.3.2 Longitudinal Compressive Strength
2.3.3 Transverse Strength
2.3.4 Shear Strength
2.3.5 Lamina Failure Theories
Maximum Stress Theory
Maximum Strain Theory
Maximum Work Theory
2.4 Mechanical Behavior of a Laminate
2.4.1 Classical Lamination Theory
2.4.2 Hygrothermal Effects
2.5 Laminate Stiffness
2.5.1 Symmetric Laminates (B = 0)
2.5.2 Anti-symmetric Laminates (A16 = A26 = D16 = D26 = 0)
2.5.3 Cross-Ply Laminates (A16 = A26 = D16 = D26 = 0)
2.5.4 Angle-Ply Laminates (with equal number of equal-thickness laminae at ±θ angles: A16 = A26 = 0)
2.5.5 Balanced Laminates (A16 = A26 = 0)
2.5.6 Specially Orthotropic Laminates (A16 = A26 = 0)
2.5.7 Quasi-Isotropic Laminates (A: isotropic)
2.6 Laminate Strength Analysis
References
Chapter 3: Laminated Composite Plates
3.1 General Formulation
3.1.1 Thin Plates
Constitutive Laws
Equilibrium Equations
Governing Equations
Boundary Conditions
3.1.2 Effects of Transverse Shear Deformation
3.1.3 High-Order Plate Theory
3.2 Symmetric Laminated Plates
3.2.1 Static Analysis
Symmetric Cross-Ply Laminates
3.2.2 Buckling and Free Vibration
Buckling
Free Vibration
3.3 MAGNETO-Electro-Elastic Laminated Plates
3.3.1 Governing Equations
3.3.2 Navier’s Solution
Remarks on Numerical Calculation
3.3.3 Levy’s Solution
Remarks on Numerical Calculation
3.3.4 Numerical Illustration
3.4 Thick Laminated Plates
3.4.1 General Formulation
Governing Equations
Governing Equations Derived from Hamilton’s Principle
3.4.2 Green’s Functions
Green’s Functions in Terms of Matrix Exponential
Explicit Solutions of Green’s Functions in Transformed Domain
Numerical Integration for Transform Integrals
Verification through Numerical Examples
References
Chapter 4: Laminated Composite Beams
4.1 General Formulation of Thin Laminated Beams
4.1.1 Narrow Beams
4.1.2 Wide Beams
4.2 Symmetric Laminated Beams
4.2.1 Static Analysis
4.2.2 Buckling and Free Vibration
Buckling
Free Vibration
4.3 Thick Laminated Beams
4.3.1 General Formulation
4.3.2 Green’s Functions
4.4 Typical Thick Beam Problems
4.4.1 Explicit Solutions
A Cantilever Beam Subjected to a Uniformly Distributed Load
A Cantilever Beam Subjected to a Concentrated Axial Force and Moment
A Simply Supported Beam Subjected to Sinusoidal Load
A Fixed-End Beam Subjected to a Concentrated Force
Some Other Typical Beam Problems
4.4.2 Numerical Results
References
Chapter 5: Laminated Composite Shells
5.1 Coordinates
5.1.1 Curvilinear Coordinates
5.1.2 Shell Coordinates
5.2 General Formulation
5.2.1 Displacement Fields
5.2.2 Strain–Displacement Relations
5.2.3 Stress Resultants and Stress Couples
5.2.4 Constitutive Laws
5.2.5 Equilibrium Equations
5.2.6 Governing Equations
5.2.7 Boundary Conditions
5.3 Shells of Revolution
5.3.1 Conical Shells
5.3.2 Circular Cylindrical Shells
5.3.3 Spherical Shells
5.3.4 Shallow Spherical Shells
5.3.5 Solution Procedure and Examples
5.4 Membrane Shells
5.4.1 Membrane Shells of Revolution
5.4.2 Axisymmetrical Load
5.4.3 Conical Membrane Shells
5.4.4 Cylindrical Membrane Shells
5.5 Vibration of Shells
References
Chapter 6: Composite Sandwich Construction
6.1 Composite Sandwich Plates
6.1.1 General Formulation
6.1.2 Buckling Analysis
Sandwiches with Symmetric Cross-Ply Laminated Faces
Rayleigh–Ritz Method
6.1.3 Free Vibration
Navier’s Solution
Levy’s Solution
Ritz Method
Orthogonality Condition
6.2 Composite Sandwich Beams
6.2.1 General Formulation
6.2.2 Buckling Analysis
6.2.3 Free Vibration
Orthogonality Condition
6.2.4 Forced Vibration
6.2.5 Vibration Suppression
Piezoelectric Sensors and Actuators
Sensor Equation
Actuator Equation
Dynamics of Feedback Control System
6.3 Composite Sandwich Cylindrical Shells
6.3.1 General Formulation
Kinematic Relations
Constitutive Laws
Equations of Motion
Composite Sandwich Circular Cylindrical Shells ( R = constant and α =  2 π)
6.3.2 Free Vibration
6.4 Delaminated Composite Sandwich Beams
6.4.1 Buckling Analysis
Perfect Composite Sandwich Beams (Without Delamination)
Delaminated Composite Beams (Without Core)
Thin Film Delamination
6.4.2 Postbuckling Analysis
6.4.3 Free Vibration
References
Chapter 7: Composite Wing Structures
7.1 Comprehensive Beam Model
7.1.1 Static Analysis
Rigid Wing Chordwise Section
Modeling of Wing Skins, Stringers, and Spar Flanges
Modeling of Spar Webs and Ribs for Multicell Wings
Equilibrium Equations and Boundary Conditions
Warping Restraint Effects
7.1.2 Dynamic Analysis
7.1.3 Matrix Form
Absence of In-Plane Spanwise Loads
7.1.4 Some Reductions
Neglect of Transverse Shear Deformation ( γ yz = 0 ⇒ β f = −w ′ f, β r = θ ′)
Neglect of Warping Restraint Effects ( ε y = v ′ 0 + zβ ′ f ⇒ λ = 0)
Reduction to Conventional Composite Sandwich Beams ( θ = β r = 0)
Reduction to Laminated Composite Beams ( θ = β r = 0, β f = − w ′ f, I x = 0)
7.2 Wings with Uniform Cross-Section
7.2.1 Free Vibration
Orthogonality Condition
7.2.2 Forced Vibration
7.2.3 Aeroelastic Divergence
7.3 Tapered Wings
7.3.1 Comprehensive Finite Element Model
7.3.2 Static Analysis
7.3.3 Free Vibration
7.3.4 Aeroelastic Divergence
7.4 Variable Thickness Plate Model
7.4.1 General Formulation
Reduction to Comprehensive Beam Model of Wing Structures
7.4.2 Finite Element Method
References
Chapter 8: Anisotropic Elasticity
8.1 Two-Dimensional Analysis
8.1.1 Stroh Formalism for Anisotropic Elastic Materials
8.1.2 Stroh Formalism in Laplace Domain for Viscoelastic Materials
8.1.3 Expanded Stroh Formalism for Piezoelectric Materials
8.1.4 Expanded Stroh Formalism for MEE Materials
8.1.5 Extended Stroh Formalism for Thermoelastic Problems
8.2 Coupled Stretching–Bending Analysis
8.2.1 Stroh-Like Formalism for General Laminated Plates
8.2.2 Specialization to Plate Bending Analysis
8.2.3 Expanded Stroh-Like Formalism for Electro-Elastic Laminates
8.2.4 Expanded Stroh-Like Formalism for MEE Laminated Plates
8.2.5 Extended Stroh-Like Formalism for Thermal Stresses in Laminates
8.3 Three-Dimensional Analysis
8.3.1 Radon–Stroh Formalism for Anisotropic Elastic Materials
8.3.2 Radon–Stroh Formalism for Anisotropic Piezoelectric and MEE Materials
8.4 Green’s Functions for Two-Dimensional Problems
8.4.1 An Infinite Anisotropic Elastic Plane
8.4.2 An Anisotropic Elastic Half-Plane
8.4.3 An Anisotropic Elastic Bi-Material
8.4.4 A Plane with an Elliptical Hole
8.4.5 A Plane with a Straight Crack
8.4.6 A Plane with an Elliptical Inclusion
Rigid Inclusion
Elastic Inclusion
8.5 Green’s Functions for Coupled Stretching–Bending Deformation
8.5.1 An Infinite Laminated Plate
8.5.2 An Infinite Laminated Plate with an Elliptical Hole
8.5.3 An Infinite Laminated Plate with a Straight Crack
8.5.4 An Infinite Laminated Plate with an Elliptical Inclusion
8.6 Green’s Functions for Three-Dimensional Problems
8.6.1 Derivatives of the Green’s Functions
8.6.2 Computation of Green’s Functions and Their Derivatives
References
Chapter 9: Numerical Methods
9.1 Finite Element Method
9.2 Boundary Element Method
9.2.1 Beam Analysis
9.2.2 Two-Dimensional Analysis
9.2.3 Coupled Stretching–Bending Analysis – Thin Plate
9.2.4 Coupled Stretching–Bending Analysis – Thick Plate
9.2.5 Three-Dimensional Analysis
9.2.6 Boundary-Based Finite Element Method
9.3 Meshless Method
9.3.1 Element-Free Galerkin (EFG) Method
9.3.2 Meshless Local Petrov–Galerkin (MLPG) Method
9.4 Numerical Examples
9.4.1 Laminated Composite Beams
9.4.2 Laminated Composite Plates
References
Author Index
Subject Index