《纺织复合材料》课程参考文献（Mechanics of Composite Materials with MATLAB）00 Contents

George Z.Voyiadjis Peter I.Kattan Mechanics of Composite Materials with MATLAB With 86 Figures and a CD ROM ②Springer

George Z. Voyiadjis Peter I. Kattan Mechanics of Composite Materials with MATLAB With 86 Figures and a CD ROM ABC

Preface This is a book for people who love mechanics of composite materials and MATLAB*.We will use the popular computer package MATLAB as a matrix calculator for doing the numerical calculations needed in mechanics of com- posite materials.In particular,the steps of the mechanical calculations will be emphasized in this book.The reader will not find ready-made MATLAB programs for use as black boxes.Instead step-by-step solutions of composite material mechanics problems are examined in detail using MATLAB.All the problems in the book assume linear elastic behavior in structural mechanics. The emphasis is not on mass computations or programming,but rather on learning the composite material mechanics computations and understanding of the underlying concepts. The basic aspects of the mechanics of fiber-reinforced composite materials are covered in this book.This includes lamina analysis in both the local and global coordinate systems,laminate analysis,and failure theories of a lamina. In the last two chapters of the book,we present a glimpse into two espe- cially advanced topics in this subject,namely,homogenization of composite materials,and damage mechanics of composite materials.The authors have deliberately left out the two topics of laminated plates and stability of com- posites as they feel these two topics are a little bit advanced for the scope of this book.In addition,each of these topics deserves a separate volume for its study and there are some books dedicated to these two topics.Each chapter starts with a summary of the basic equations.This is followed by the MAT- LAB functions which are specific to the chapter.Then,a number of examples is solved demonstrating both the theory and numerical computations.The examples are of two types:the first type is theoretical and involves deriva- tions and proofs of various equations,while the other type is MATLAB-based and involves using MATLAB in the calculations.A total of 44 special MAT- LAB functions for composite material mechanics are provided as M-files on the accompanying CD-ROM to be used in the examples and solution of the MATLAB is a registered trademark of the MathWorks,Inc

Preface This is a book for people who love mechanics of composite materials and MATLAB∗. We will use the popular computer package MATLAB as a matrix calculator for doing the numerical calculations needed in mechanics of com￾posite materials. In particular, the steps of the mechanical calculations will be emphasized in this book. The reader will not find ready-made MATLAB programs for use as black boxes. Instead step-by-step solutions of composite material mechanics problems are examined in detail using MATLAB. All the problems in the book assume linear elastic behavior in structural mechanics. The emphasis is not on mass computations or programming, but rather on learning the composite material mechanics computations and understanding of the underlying concepts. The basic aspects of the mechanics of fiber-reinforced composite materials are covered in this book. This includes lamina analysis in both the local and global coordinate systems, laminate analysis, and failure theories of a lamina. In the last two chapters of the book, we present a glimpse into two espe￾cially advanced topics in this subject, namely, homogenization of composite materials, and damage mechanics of composite materials. The authors have deliberately left out the two topics of laminated plates and stability of com￾posites as they feel these two topics are a little bit advanced for the scope of this book. In addition, each of these topics deserves a separate volume for its study and there are some books dedicated to these two topics. Each chapter starts with a summary of the basic equations. This is followed by the MAT￾LAB functions which are specific to the chapter. Then, a number of examples is solved demonstrating both the theory and numerical computations. The examples are of two types: the first type is theoretical and involves deriva￾tions and proofs of various equations, while the other type is MATLAB-based and involves using MATLAB in the calculations. A total of 44 special MAT￾LAB functions for composite material mechanics are provided as M-files on the accompanying CD-ROM to be used in the examples and solution of the ∗ MATLAB is a registered trademark of the MathWorks, Inc

VIII Preface problems.These MATLAB functions are specifically written by the authors to be used with this book.These functions have been tested successfully with MATLAB versions 6.0 and 6.2.They should work with other later or previous versions.Each chapter also ends with a number of problems to be used as practice for students. The book is written primarily for students studying mechanics of compos- ite materials for the first time.The book is self-contained and can be used as a textbook for an introductory course on mechanics of composite materials. Since the computations of composite materials usually involve matrices and matrix manipulations,it is only natural that students use a matrix-based soft- ware package like MATLAB to do the calculations.In fact the word MATLAB stands for MATrix LABoratory. The main features of this book are listed as follows: 1.The book is divided into twelve chapters that are well defined and cor- related.Each chapter is written in a way to be consistent with the other chapters. 2.The book includes a short tutorial on using MATLAB in Chap.1. 3.The CD-ROM that accompanies the book includes 44 MATLAB func- tions(M-files)that are specifically written by the authors to be used with this book.These functions comprise what may be called the MATLAB Composite Material Mechanics Toolbox.It is used mainly for problems in structural mechanics.The provided MATLAB functions are designed to be simple and easy to use. 4.The book stresses the interactive use of MATLAB.The MATLAB examples are solved in an interactive manner in the form of interactive sessions with MATLAB.No ready-made subroutines are provided to be used as black boxes.These latter ones are available in other books and on the internet. 5.Some of the examples show in detail the derivations and proofs of various basic equations in the study of the mechanics of composite materials.The derivations of the remaining equations are left to some of the problems. 6.Solutions to most of the problems are included in a special section at the end of the book.These solutions are detailed especially for the first six chapters. The authors wish to thank the editors at Springer-Verlag (especially Dr.Thomas Ditzinger)for their cooperation and assistance during the writ- ing of this book.Special thanks are also given to our family members without their support and encouragement this book would not have been possible. The second author would also like to acknowledge the financial support of the Center for Computation and Technology headed by Edward Seidel at Louisiana State University. Louisiana State University George Z.Voyiadjis February 2005 Peter I.Kattan

VIII Preface problems. These MATLAB functions are specifically written by the authors to be used with this book. These functions have been tested successfully with MATLAB versions 6.0 and 6.2. They should work with other later or previous versions. Each chapter also ends with a number of problems to be used as practice for students. The book is written primarily for students studying mechanics of compos￾ite materials for the first time. The book is self-contained and can be used as a textbook for an introductory course on mechanics of composite materials. Since the computations of composite materials usually involve matrices and matrix manipulations, it is only natural that students use a matrix-based soft￾ware package like MATLAB to do the calculations. In fact the word MATLAB stands for MATrix LABoratory. The main features of this book are listed as follows: 1. The book is divided into twelve chapters that are well defined and cor￾related. Each chapter is written in a way to be consistent with the other chapters. 2. The book includes a short tutorial on using MATLAB in Chap. 1. 3. The CD-ROM that accompanies the book includes 44 MATLAB func￾tions (M-files) that are specifically written by the authors to be used with this book. These functions comprise what may be called the MATLAB Composite Material Mechanics Toolbox. It is used mainly for problems in structural mechanics. The provided MATLAB functions are designed to be simple and easy to use. 4. The book stresses the interactive use of MATLAB. The MATLAB examples are solved in an interactive manner in the form of interactive sessions with MATLAB. No ready-made subroutines are provided to be used as black boxes. These latter ones are available in other books and on the internet. 5. Some of the examples show in detail the derivations and proofs of various basic equations in the study of the mechanics of composite materials. The derivations of the remaining equations are left to some of the problems. 6. Solutions to most of the problems are included in a special section at the end of the book. These solutions are detailed especially for the first six chapters. The authors wish to thank the editors at Springer-Verlag (especially Dr. Thomas Ditzinger) for their cooperation and assistance during the writ￾ing of this book. Special thanks are also given to our family members without their support and encouragement this book would not have been possible. The second author would also like to acknowledge the financial support of the Center for Computation and Technology headed by Edward Seidel at Louisiana State University. Louisiana State University George Z. Voyiadjis February 2005 Peter I. Kattan

Contents 1 Introduction.…· 1 1.1 Mechanics of Composite Materials......................... 2 1.2 MATLAB Functions for Mechanics of Composite Materials .. 2 l.3 MATLAB Tutorial… 3 2 Linear Elastic Stress-Strain Relations...................... 9 2.1 Basic Equations......................................... 9 2.2 MATLAB Functions Used................................ 13 Example2.1… 15 MATLAB Example 2.2............................. 16 MATLAB Example 2.3............................. 19 Problems...............................................21 3 Elastic Constants Based on Micromechanics,…· 25 3.1 Basic Equations.…… 25 3.2 MATLAB Functions Used ...... 29 Example 3.1......... 32 MATLAB Example 3.2 33 ATLAB Example3.3......……· 35 Problems............................................... 43 4 Plane Stress...................... 47 4.1 Basic Equations......................................... 47 4.2 MATLAB Functions Used ............................... 49 Example 4.1......... 50 MATLAB Example 4.2............................. 51 MATLAB Example 4.3............................. 52 Problems.………… 53

Contents 1 Introduction ............................................... 1 1.1 Mechanics of Composite Materials . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 MATLAB Functions for Mechanics of Composite Materials . . . 2 1.3 MATLAB Tutorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Linear Elastic Stress-Strain Relations ...................... 9 2.1 Basic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 MATLAB Functions Used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Example 2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 MATLAB Example 2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 MATLAB Example 2.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3 Elastic Constants Based on Micromechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.1 Basic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2 MATLAB Functions Used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Example 3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 MATLAB Example 3.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 MATLAB Example 3.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4 Plane Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.1 Basic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.2 MATLAB Functions Used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Example 4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 MATLAB Example 4.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 MATLAB Example 4.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

X Contents 5 Global Coordinate System ................................ 57 5.1 Basic Equations .................. 57 5.2 MATLAB Functions Used ...... 60 Example5.1......... 62 MATLAB Example 5.2.............................63 MATLAB Example 5.3............................. 72 Problems .............................................. 75 6 Elastic Constants Based on Global Coordinate System...... 79 6.1 Basic Equations.......... 79 6.2 MATLAB Functions Used................................ 80 Example 6.1 ........... 84 MATLAB Example 6.2............................. 84 MATLAB Example 6.3.............................102 Problems................112 7 Laminate Analysis -Part I................................115 7.1 Basic Equations....................115 7.2 MATLAB Functions Used....... ....119 MATLAB Example7.1.… ...120 MATLAB Example 7.2................... ·..130 Problems................... ….145 8 Laminate Analysis -Part II...............................149 8.1 Basic Equations........··· ………………...149 8.2 MATLAB Functions Used................................152 Example 8.1......... ……..153 MATLAB Example 8.2.. ..155 MATLAB Example 8.3.................... ….160 Problems..................166 9 Effective Elastic Constants of a Laminate..................169 9.1 Basic Equations.....................169 9.2 MATLAB Functions Used................................170 Example 9.1 ............................ ....172 MATLAB Example 9.2.............................173 MATLAB Example 9.3.................... ..176 Problems.. ....181 10 Failure Theories of a Lamina..............................183 10.1 Basic Equations..................183 10.1.1 Maximum Stress Failure Theory.....................184 10.1.2 Maximum Strain Failure Theory ....................186

X Contents 5 Global Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.1 Basic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.2 MATLAB Functions Used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Example 5.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 MATLAB Example 5.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 MATLAB Example 5.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 6 Elastic Constants Based on Global Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 6.1 Basic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 6.2 MATLAB Functions Used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Example 6.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 MATLAB Example 6.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 MATLAB Example 6.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 7 Laminate Analysis – Part I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 7.1 Basic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 7.2 MATLAB Functions Used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 MATLAB Example 7.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 MATLAB Example 7.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 8 Laminate Analysis – Part II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 8.1 Basic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 8.2 MATLAB Functions Used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 Example 8.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 MATLAB Example 8.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 MATLAB Example 8.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 9 Effective Elastic Constants of a Laminate . . . . . . . . . . . . . . . . . . 169 9.1 Basic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 9.2 MATLAB Functions Used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 Example 9.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 MATLAB Example 9.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 MATLAB Example 9.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 10 Failure Theories of a Lamina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 10.1 Basic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 10.1.1 Maximum Stress Failure Theory . . . . . . . . . . . . . . . . . . . . . 184 10.1.2 Maximum Strain Failure Theory . . . . . . . . . . . . . . . . . . . . 186

Contents XI 10.1.3 Tsai-Hill Failure Theory.............. ..187 10.1.4 Tsai-Wu Failure Theory............................189 11 Introduction to Homogenization of Composite Materials............. ....193 11.1 Eshelby Method................ ..193 Problems...............195 12 Introduction to Damage Mechanics of Composite Materials....................................197 12.1 Basic Equations .............. …..197 12.2 Overall Approach.......... ……..198 12.3 Local Approach .....200 12.4 Final Remarks ... ....201 Problems...... ...203 Solutions to Problems....... ...205 References..................... .....329 Contents of the Accompanying CD-ROM......................331 Index

Contents XI 10.1.3 Tsai-Hill Failure Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 10.1.4 Tsai-Wu Failure Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 11 Introduction to Homogenization of Composite Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 11.1 Eshelby Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 12 Introduction to Damage Mechanics of Composite Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 12.1 Basic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 12.2 Overall Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 12.3 Local Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 12.4 Final Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 Solutions to Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 Contents of the Accompanying CD-ROM . . . . . . . . . . . . . . . . . . . . . . 331 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333