第1页 / 共336页
第2页 / 共336页
第3页 / 共336页
第4页 / 共336页
第5页 / 共336页
第6页 / 共336页
第7页 / 共336页
第8页 / 共336页
MechanicsOfCompositeMaterialsWithMatlab.pdf 英文原版
George Z. Voyiadjis Peter I. Kattan
Mechanics of
Composite Materials
with
MATLAB
With 86 Figures and a CD ROM
ABC
http://freepdf-books.comhttp://freepdf-books.com
Prof. George Z. Voyiadjis
Prof. Peter I. Kattan
Louisiana State University
Dept.Civil and Environmental Engineering
Baton Rouge, LA 70803, USA
e-mail: voyiadjis@eng.lsu.edu
pkattan@lsu.edu
Library of Congress Control Number: 2005920509
ISBN -10 3-540-24353-4 Springer Berlin Heidelberg New York
ISBN -13 978-3-540-24353-3 Springer Berlin Heidelberg New York
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is
concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting,
reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication
or parts thereof is permitted only under the provisions of the German Copyright Law of September 9,
1965, in its current version, and permission for use must always be obtained from Springer. Violations are
liable for prosecution under the German Copyright Law.
Springer is a part of Springer Science+Business Media
springeronline.com
c Springer-Verlag Berlin Heidelberg 2005
Printed in The Netherlands
The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply,
even in the absence of a specific statement, that such names are exempt from the relevant protective laws
and regulations and therefore free for general use.
Typesetting: by the authors and TechBooks using a Springer LATEX macro package
Cover design: deblik, Berlin
Printed on acid-free paper
SPIN: 11015482
89/3141/jl
5 4 3 2 1 0
http://freepdf-books.comhttp://freepdf-books.com
Dedicated with Love to CHRISTINA, ELENA, and ANDREW
George Z. Voyiadjis
Dedicated with Love to My Family
Peter I. Kattan
http://freepdf-books.comhttp://freepdf-books.com
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.
http://freepdf-books.comhttp://freepdf-books.com
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
February 2005
George Z. Voyiadjis
Peter I. Kattan
http://freepdf-books.comhttp://freepdf-books.com
Contents
1
2
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Mechanics of Composite Materials . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 MATLAB Functions for Mechanics of Composite Materials . . .
1.3 MATLAB Tutorial
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1
2
3
9
Linear Elastic Stress-Strain Relations . . . . . . . . . . . . . . . . . . . . . .
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
http://freepdf-books.comhttp://freepdf-books.com
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
8
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
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
http://freepdf-books.comhttp://freepdf-books.com
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
http://freepdf-books.comhttp://freepdf-books.com
相关推荐
2023年江西萍乡中考道德与法治真题及答案.doc
2012年重庆南川中考生物真题及答案.doc
2013年江西师范大学地理学综合及文艺理论基础考研真题.doc
2020年四川甘孜小升初语文真题及答案I卷.doc
2020年注册岩土工程师专业基础考试真题及答案.doc
2023-2024学年福建省厦门市九年级上学期数学月考试题及答案.doc
2021-2022学年辽宁省沈阳市大东区九年级上学期语文期末试题及答案.doc
2022-2023学年北京东城区初三第一学期物理期末试卷及答案.doc
2018上半年江西教师资格初中地理学科知识与教学能力真题及答案.doc
2012年河北国家公务员申论考试真题及答案-省级.doc
2020-2021学年江苏省扬州市江都区邵樊片九年级上学期数学第一次质量检测试题及答案.doc
2022下半年黑龙江教师资格证中学综合素质真题及答案.doc
