With rapid growth of the use of composite materials in many commercial products ranging from sports equipment to high-performance aircraft, literature on composite materials has proliferated. At the time of the publication of this book a simple search of a popular web site for books with the words "composite materials" in their title yielded more than 250 entries. Many of these titles are well-written textbooks on mechanics of composite materials and have been adopted by educational institutions for introductory courses. As the application of composites to commercial products has increased, so has the need for literature that focuses on the design aspects of these materials. However, the number of titles that focus on the mechanics of composites far outnumbers those dealing with design. In particular, books that focus on optimal design of composite materials virtually do not exist. It is the intent of this book to introduce readers to the emerging field of optimal design of laminated composite materials.
The first and the foremost reason for writing this book was the desire to acquaint students with the latest techniques in the field. For many years, designers have treated optimization problems involving composite materials with continuous optimization techniques that were ill suited for these problems. The design of a composite laminate stacking sequence generally involves selecting discrete layer thickness and orientation angles - a discrete optimization problem. Researchers in this field have more recently focused on numerical and graphical methods useful for the solution of such problems; this book mirrors that focus. In particular, the book places emphasis on graphical design techniques developed by Professor Miki from Japan. These techniques allow representation of even the most complicated stacking sequences using two parameters bounded by a parabola and provide extremely valuable insight into the multiplicity of solutions available for laminate design problems.
Another important motivation for the book was the need to provide condensed coverage that would be of use to the design engineer. Design of composite materials and structures requires both a thorough understanding of the mechanics of laminated composites and familiarity with optimization techniques that enable designers to find practical laminate configurations in an efficient manner. At present, a student wanting to learn about the application of optimization techniques to composite design will need to take a separate course in each subject. This is somewhat difficult within the constraints of an undergraduate curriculum. The book combines the study of the mechanics of composite laminates with optimization methods that are most useful for the design of such laminates.
This book has been developed for senior-level undergraduate or early graduate courses in numerical design methods for laminated composite materials. Applications of composite materials have traditionally originated in weight-critical aerospace structures. More recently, these materials have become popular in civil engineering infrastructure applications (such as bridge and building construction) and mechanical engineering applications (such as mechanisms and lightweight robotic structures). Therefore, the book may be used in aerospace engineering, civil engineering, engineering science and mechanics, and mechanical engineering curricula. In addition, the book has technical material useful for practicing engineers in related fields. Researchers in composite materials are likely to benefit from state of the art methods introduced in the book.
The first chapter reviews the types of composite materials in use and the terminology established for their description. The types of composites considered in this book are then identified and their properties are discussed within the context of mechanics. A brief review of the design issues relevant to composite materials is included. The chapter concludes with an introduction to the terminology and formulation of mathematical optimization problems, with special emphasis on laminate design problems.
The second and third chapters introduce the basic equations and assumptions used in the analysis of laminated composites under mechanical and thermal loads. They emphasize the computation of elastic properties as functions of variables that can be changed during the design process and the effects of such changes on response quantities such as stresses and strains.
Chapter 4 formulates the in-plane stiffness design as an optimization problem and introduces a simple graphical technique for its solution. Also provided is a technique to handle the discrete nature of the thickness and orientation design variables.
Two formal procedures, namely integer linear programming and genetic algorithms, suitable for handling discrete optimization problems specific to composite laminate design are introduced in Chapter 5. In particular, the formulation and solution of the in-plane stiffness design problem is demonstrated.
Chapters 6 and 7 address strength analysis and design, respectively. Commonly used failure criteria for laminated composite materials and their implementation for strength analyses are introduced in Chapter 6. Chapter 7 describes the implementation of strength constraints in design optimization based on graphical and mathematical optimization procedures.
Finally, Chapter 8 introduces analysis and design for bending requirements. These include the transverse displacement of a simply supported laminate loaded by transverse loads, its natural vibration frequencies, and the buckling response of a simply supported laminate under in-plane loads.
We have used the material in our respective institutions for a combined senior-level undergraduate and first-year graduate course for several years. For a one-semester course with students who have no previous background in composites or optimization, we recommend that the course cover most of the material in Chapters 1, 2, 4, and 5, and parts of Chapter 6. In addition, it is probably possible to cover material from one more chapter. Depending on the emphasis of the course, Chapters 3, 7, or 8, which focus on thermomechanical, strength, or bending design characteristics, respectively, may be added. It is also possible to cover a combination of sections from the remaining chapters as the instructor sees fit.
The authors wish to express their appreciation for many valuable suggestions from former students in courses that led to the development of this book. Thanks also go to the authors' respective universities for providing the opportunities to teach courses directly relevant to the book's content, and their fellow faculty members for providing valuable input and stimulating discussions. Special thanks are also due Professor Mitsunori Miki of the Doshisha University, Japan for introducing us to the graphical representation of laminate optimization problems, which is heavily used in the book. The authors also appreciate the input and suggestions provided by various individuals, in particular, Professor Valery V. Vasiliev of Moscow State University of Aviation Technology, Professor Ron Kander of Virginia Tech, Professor Günay Anlas of Bogazici University, Dr. Walter Dauksher of Boeing, for reviewing some of the chapters of the book. The authors would also like to thank Dr. James H. Starnes, Jr., of NASA Langley Research Center. He has sponsored research leading to many of the results reported in the textbook, and his insight into design issues for composite materials enriched our appreciation of the subject.
Zafer Gürdal
Raphael T. Haftka
Prabhat Hajela