具体描述
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; and, additional exercises and examples. No 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 non-linear finite element models of plate and shell laminated composite structures.
纤维增强复合材料结构力学导论：从宏观到微观的深入解析 本书旨在为结构工程师、材料科学家以及研究生提供一本全面而深入的关于纤维增强复合材料结构力学分析的教科书。内容聚焦于理解这些先进材料在复杂载荷条件下的行为，着重于从基础的本构关系到复杂的非线性效应的系统性阐述。本书的叙述风格力求严谨，注重理论的推导过程与实际工程应用的紧密结合，避免过度依赖简化模型而牺牲物理机制的准确性。 本书共分十二章，结构清晰，逻辑递进。 第一部分：基础理论与本构关系（第1章至第3章） 第1章：先进复合材料概述与微观力学基础 本章首先对当前工程中应用的主要高性能复合材料体系（如碳纤维、玻璃纤维、芳纶纤维与环氧树脂、聚合物基体）的优势与局限性进行比较分析。随后，深入探讨纤维与基体之间的界面行为，这是决定宏观材料性能的关键因素。重点阐述“混合律”（Rule of Mixtures）的适用范围及其修正模型，包括张量形式的弹性常数推导，如杨氏模量、剪切模量和泊松比的各向异性表达。本章的理论基础奠定在均匀化方法（Homogenization Technique）之上，为后续分析提供必要的数学工具。 第2章：单层板的弹性分析与应力-应变关系 本章集中于正交各向异性材料单层板的本构关系。详细推导了基于平面应力假设的本构方程，并清晰界定了材料坐标系（Material Coordinates）与构件坐标系（Laminate Coordinates）之间的坐标变换。重点分析了$90^circ$、$pm 45^circ$铺层在双轴拉伸和纯剪切载荷下的响应特性。引入了张量旋转公式，并辅以大量的实例说明如何计算任意角度纤维方向下的工程弹性常数，如$Q_{11}, Q_{12}, Q_{66}$等平面刚度系数。本章强调了应力奇点和局部应力集中现象在含孔或载荷集中区域的预估方法。 第3章：经典层合板理论（CLT）的精确推导与应用 本章是全书的核心之一，系统地推导了经典层合板理论（Classical Lamination Theory, CLT）。推导过程严格基于Kirchhoff-Love假设，但对位移场函数的选取进行了细致的讨论，确保了理论的严密性。本章详细阐述了由应变和曲率决定的面内力（$N_x, N_y, N_{xy}$）和面外力矩（$M_x, M_y, M_{xy}$）与应力状态之间的关系。核心内容包括刚度矩阵$[A], [B], [D]$的建立，其中对$[B]$矩阵（耦合矩阵）的物理意义进行了深入剖析，阐明了其在材料轴与几何轴不一致时产生的热弯曲和耦合效应。最后，给出了CLT在求解简单边界条件下的精确解算流程。 第二部分：几何效应与稳定性分析（第4章至第7章） 第4章：更精细的层合板理论：一阶剪切变形理论（FSDT） 认识到CLT在厚板或高模量材料结构中对剪切变形的忽略所带来的局限性，本章引入了Mindlin-Reissner型的一阶剪切变形理论（First-order Shear Deformation Theory, FSDT）。详细讨论了FSDT相对于CLT的改进之处，特别是如何通过引入一个剪切应变自由度来更准确地描述厚度方向上的应力分布。本章着重分析了剪切锁定（Shear Locking）现象及其在FSDT中的数值处理方法，并提出了剪切修正因子的选择准则。 第5章：轴对称与旋转壳体的力学建模 本章将理论扩展到旋转对称结构，如火箭和导弹结构中常见的轴对称复合材料壳体。重点讨论了Donnell和Love-Kirchhoff壳体理论在复合材料中的修正应用。针对复合材料固有的各向异性，详细推导了具有耦合效应的厚度方向上的应力分层计算方法，并分析了层间剪切应力在壳体中如何影响疲劳寿命。 第6章：线性屈曲分析与临界载荷的确定 本章聚焦于复合材料结构的稳定性问题。线性屈曲分析是本章的基础，推导了基于欧拉梁、板壳理论的特征值问题。针对层合板，重点分析了铺层角度对临界屈曲载荷的显著影响，特别是轴向压缩和双轴压缩下的屈曲模式。详细讨论了边界条件对临界载荷的影响，并引入了非线性稳定性分析的预备知识，如初始几何缺陷对屈曲性能的影响。 第7章：基于能量法的变分原理与有限元基础 本章从理论深度上探讨了复合材料结构分析的统一框架——虚功原理和最小势能原理。以瑞利-里茨法为例，展示了如何利用能量泛函来推导更复杂的边值问题。作为过渡章节，本章简要介绍了复合材料单元的构建基础，重点讨论了高阶有限元方法中如何处理剪切锁定，以及如何在单元刚度矩阵中正确体现$[A], [B], [D]$矩阵的耦合效应。 第三部分：先进分析与非线性效应（第8章至第12章） 第8章：层间断裂力学与疲劳分析 复合材料结构失效的常见模式是层间脱粘。本章深入层间断裂力学，引入了能量释放率（Strain Energy Release Rate, $G$）的概念。详细讨论了Mode I, II, III混合模式的断裂分析，并介绍了遵循拜尔伦（Benzegg-Lundell）准则的层间强度评估方法。此外，本章还专门探讨了复合材料在循环载荷下的疲劳累积损伤模型，包括Goodman图和Miner法则的复合材料适用性修正。 第9章：非线性几何效应与大变形分析 当结构发生大变形或承受高载荷时，必须考虑几何非线性。本章主要关注几何刚度对屈曲和后屈曲行为的影响。推导了二阶应变张量，并将其代入能量泛函中，从而得到包含二次非线性项的平衡方程。重点分析了轴向压缩下的拉压不对称性导致的几何非线性效应。 第10章：热力耦合分析与冲击响应 现代结构往往需要在极端温度环境下工作。本章探讨了热应力在各向异性材料中的分布规律，推导了考虑热膨胀系数的温度场对结构应力的贡献。随后，本章转向动态响应，详细分析了冲击载荷（如碰撞）下的瞬态分析，利用模态叠加法和步进积分方法求解运动方程，并探讨了纤维和基体的粘弹性行为对冲击能量吸收的影响。 第11章：粘弹性与蠕变行为 对于长期服役或在高温环境下工作的聚合物基复合材料，蠕变和应力松弛是重要的性能衰减因素。本章引入了粘弹性本构理论，如Maxwell模型和Kelvin-Voigt模型，并使用松弛或蠕变柔量函数来描述时间依赖性。重点阐述了如何将这些时间依赖性本构关系纳入到更高级的有限元框架中进行长期寿命预测。 第12章：高级铺层设计与优化原理 本章将理论应用于设计实践。讨论了实现特定结构性能（如零热膨胀、特定模态抑制）的铺层设计策略。引入了目标驱动的结构优化概念，包括最小化重量下的刚度最大化问题。最后，对先进的智能材料集成复合材料（如压电耦合复合材料）的本构模型进行了概述，展望了未来复合材料结构分析的发展方向。 全书配有大量的数学推导、清晰的图示和适量的算例，旨在使读者不仅掌握计算方法，更能深刻理解复合材料在不同物理场耦合下的内在力学行为。
作者简介
目录信息
Equations of Anisotropic Elasticity, Virtual Work Principles, and Variational Methods
Fiber-Reinforced Composite Materials
Mathematical Preliminaries
Equations of Anisotropic Entropy
Virtual Work Principles
Variational Methods
Summary
Introduction to Composite Materials
Basic Concepts and Terminology
Constitutive Equations of a Lamina
Transformation of Stresses and Strains
Plan Stress Constitutive Relations
Classical and First-Order Theories of Laminated Composite Plates
Introduction
An Overview of Laminated Plate Theories
The Classical Laminated Plate Theory
The First-Order Laminated Plate Theory
Laminate Stiffnesses for Selected Laminates
One-Dimensional Analysis of Laminated Composite Plates
Introduction
Analysis of Laminated Beams Using CLPT
Analysis of Laminated Beams Using FSDT
Cylindrical Bending Using CLPT
Cylindrical Bending Using FSDT
Vibration Suppression in Beams
Closing Remarks
Analysis of Specially Orthotropic Laminates Using CLPT
Introduction
Bending of Simply Supported Rectangular Plates
Bending of Plates with Two Opposite Edges Simply Supported
Bending of Rectangular Plates with Various Boundary Conditions
Buckling of Simply Supported Plates Under Compressive Loads
Buckling of Rectangular Plates Under In-Plane Shear Load
Vibration of Simply Supported Plates
Buckling and Vibration of Plates with Two Parallel Edges Simply Supported
Transient Analysis
Closure
Analytical Solutions of Rectangular Laminated Plates
Using CLPT
Governing Equations in Terms of Displacements
Admissible Boundary Conditions for the Navier Solutions
Navier Solutions of Antisymmetric Cross-Ply Laminates
Navier Solutions of Antisymmetric Angle-Ply Laminates
The Levy Solutions
Analysis of Midplane Symmetric Laminates
Transient Analysis
Summary
Analytical Solutions of Rectangular Laminated Plates Using FSDT
Introduction
Simply Supported Antisymmetric Cross-Ply Laminated Plates
Simply Supported Antisymmetric Angle-Ply Laminated Plates
Antisymmetric Cross-Ply Laminates with Two Opposite Edges Simply Supported
Antisymmetric Angle-Ply Laminates with Two Opposite Edges Simply Supported
Transient Solutions
Vibration Control of Laminated Plates
Summary
Theory and Analysis of Laminated Shells
Introduction
Governing Equations
Theory of Doubly-Curved Shell
Vibration and Buckling of Cross-Ply Laminated Circular Cylindrical Shells
Linear Finite Element Analysis of Composite Plates and Shells
Introduction
Finite Element Models of the Classical Plate Theory (CLPT)
Finite Element Models of Shear Deformation Plate Theory (FSDT)
Finite Element Analysis of Shells
Summary
Nonlinear Analysis of Composite Plates and Shells
Introduction
Classical Plate Theory
First-Order Shear Deformation Plate Theory
Time Approximation and the Newton-Raphson Method
Numerical Examples of Plates
Functionally Graded Plates
Finite Element Models of Laminated Shell Theory
Continuum Shell Finite Element
Postbuckling Response and Progressive Failure of Composite Panels in Compression
Closure
Third-Order Theory of Laminated Composite Plates and Shells
Introduction
A Third-Order Plate Theory
Higher-Order Laminate Stiffness Characteristics
The Navier Solutions
Levy Solutions of Cross-Ply Laminates
Finite Element Model of Plates
Equations of Motion of the Third-Order Theory of Doubly-Curved Shells
Layerwise Theory and Variable Kinematic Model
Introduction
Development of the Theory
Finite Element Model
Variable Kinematic Formulations
Application to Adaptive Structures
Layerwise Theory of Cylindrical Shell
Closure
Subject Index
· · · · · · (收起)
Fiber-Reinforced Composite Materials
Mathematical Preliminaries
Equations of Anisotropic Entropy
Virtual Work Principles
Variational Methods
Summary
Introduction to Composite Materials
Basic Concepts and Terminology
Constitutive Equations of a Lamina
Transformation of Stresses and Strains
Plan Stress Constitutive Relations
Classical and First-Order Theories of Laminated Composite Plates
Introduction
An Overview of Laminated Plate Theories
The Classical Laminated Plate Theory
The First-Order Laminated Plate Theory
Laminate Stiffnesses for Selected Laminates
One-Dimensional Analysis of Laminated Composite Plates
Introduction
Analysis of Laminated Beams Using CLPT
Analysis of Laminated Beams Using FSDT
Cylindrical Bending Using CLPT
Cylindrical Bending Using FSDT
Vibration Suppression in Beams
Closing Remarks
Analysis of Specially Orthotropic Laminates Using CLPT
Introduction
Bending of Simply Supported Rectangular Plates
Bending of Plates with Two Opposite Edges Simply Supported
Bending of Rectangular Plates with Various Boundary Conditions
Buckling of Simply Supported Plates Under Compressive Loads
Buckling of Rectangular Plates Under In-Plane Shear Load
Vibration of Simply Supported Plates
Buckling and Vibration of Plates with Two Parallel Edges Simply Supported
Transient Analysis
Closure
Analytical Solutions of Rectangular Laminated Plates
Using CLPT
Governing Equations in Terms of Displacements
Admissible Boundary Conditions for the Navier Solutions
Navier Solutions of Antisymmetric Cross-Ply Laminates
Navier Solutions of Antisymmetric Angle-Ply Laminates
The Levy Solutions
Analysis of Midplane Symmetric Laminates
Transient Analysis
Summary
Analytical Solutions of Rectangular Laminated Plates Using FSDT
Introduction
Simply Supported Antisymmetric Cross-Ply Laminated Plates
Simply Supported Antisymmetric Angle-Ply Laminated Plates
Antisymmetric Cross-Ply Laminates with Two Opposite Edges Simply Supported
Antisymmetric Angle-Ply Laminates with Two Opposite Edges Simply Supported
Transient Solutions
Vibration Control of Laminated Plates
Summary
Theory and Analysis of Laminated Shells
Introduction
Governing Equations
Theory of Doubly-Curved Shell
Vibration and Buckling of Cross-Ply Laminated Circular Cylindrical Shells
Linear Finite Element Analysis of Composite Plates and Shells
Introduction
Finite Element Models of the Classical Plate Theory (CLPT)
Finite Element Models of Shear Deformation Plate Theory (FSDT)
Finite Element Analysis of Shells
Summary
Nonlinear Analysis of Composite Plates and Shells
Introduction
Classical Plate Theory
First-Order Shear Deformation Plate Theory
Time Approximation and the Newton-Raphson Method
Numerical Examples of Plates
Functionally Graded Plates
Finite Element Models of Laminated Shell Theory
Continuum Shell Finite Element
Postbuckling Response and Progressive Failure of Composite Panels in Compression
Closure
Third-Order Theory of Laminated Composite Plates and Shells
Introduction
A Third-Order Plate Theory
Higher-Order Laminate Stiffness Characteristics
The Navier Solutions
Levy Solutions of Cross-Ply Laminates
Finite Element Model of Plates
Equations of Motion of the Third-Order Theory of Doubly-Curved Shells
Layerwise Theory and Variable Kinematic Model
Introduction
Development of the Theory
Finite Element Model
Variable Kinematic Formulations
Application to Adaptive Structures
Layerwise Theory of Cylindrical Shell
Closure
Subject Index
· · · · · · (收起)
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