Finite Element Analysis of Composite Materials deals with the analysis of structures made of composite materials, also called composites. The analysis of composites treated in this textbook includes the analysis of the material itself, at the micro-level, and the analysis of structures made of composite materials. This textbook evolved from the class notes of MAE 646 Advanced Mechanics of Composite Materials that I teach as a graduate course at West Virginia University. Although this is also a textbook on advanced mechanics of composite materials, the use of the finite element method is essential for the solution of the complex boundary value problems encountered in the advanced analysis of composites, and thus the title of the book.
There are a number of good textbooks on advanced mechanics of composite materials, but none carries the theory to a practical level by actually solving problems, as it is done in this textbook. Some books devoted exclusively to finite element analysis include some examples about modeling composites but fall quite short of dealing with the actual analysis and design issues of composite materials and composite structures. This textbook includes an explanation of the concepts involved in the detailed analysis of composites, a sound explanation of the mechanics needed to translate those concepts into a mathematical representation of the physical reality, and a detailed explanation of the solution of the resulting boundary value problems by using commercial Finite Element Analysis software such as ANSYS™. Furthermore, this textbook includes more than fifty fully developed examples interspersed with the theory, as well as more than seventy-five exercises at the end of chapters, and more than fifty separate pieces of ANSYS code used to explain in detail the solution of example problems. The reader will be able to reproduce the examples and complete the exercises. When a finite element analysis is called for, the reader will be able to do it with commercially or otherwise available software. A web site is set up with links to download the necessary software unless it is easily available from Finite Element Analysis software vendors. ANSYS and MATLAB™ code is explained in the examples, and the code can be downloaded from the web site as well. Furthermore, the reader will be able to extend the capabilities of ANSYS by use of ANSYS Parametric Design Language (APDL), user material subroutines, and programmable post-processing, as demonstrated in the examples included in this textbook.
Chapters 1 through 8 can be covered in a one-semester graduate course. Chapter 2 (Introduction to the Finite Element Method) contains a brief introduction intended for those readers who have not had a formal course or prior knowledge about the finite element method. Chapter 4 (Buckling) is not referenced in the remainder of the textbook and thus it could be omitted in favor of more exhaustive coverage of content in later chapters. Chapters 7 (Viscoelasticity) and 8 (Damage) are placed consecutively to emphasize hereditary phenomena. However, Viscoelasticity can be skipped if more emphasis on Damage and/or Delaminations is desired in a one-semester course. A complete continuum damage model with coupled damage-plasticity effects is presented in Chapter 9, immediately following the more fundamental treatment of Damage in Chapter 8. Chapter 9 could be omitted for the sake of time, especially if the instructor desires to cover Chapter 10 (Delaminations) as part of a one-semester course.
The inductive method is applied as much as possible in this textbook. That is, topics are introduced with examples of increasing complexity, until sufficient physical understanding is reached to introduce the general theory without difficulty. This method will sometimes require that, at earlier stages of the presentation, certain facts, models, and relationships be accepted as fact, until they are completely proven later on. For example, in Chapter 7, viscoelastic models are introduced early to aid the reader in gaining an appreciation for the response of viscoelastic materials. This is done simultaneously with a cursory introduction to the superposition principle and the Laplace transform, which are formally introduced only later in the chapter. For those readers accustomed to the deductive method, this may seem odd, but many years of teaching have convinced me that students acquire and retain knowledge more efficiently in this way.
It is assumed that the reader is familiar with basic mechanics of composites as covered in introductory level textbooks such as my previous textbook Introduction to Composite Material Design. Furthermore, it is assumed that the reader masters a body of knowledge that is commonly acquired as part of a bachelor of science degree in any of the following disciplines: Aerospace, Mechanical, Civil, or similar. References to books and to other sections in this textbook, as well as footnotes are used to assist the reader in refreshing those concepts and to clarify the notation used. Prior knowledge of continuum mechanics, tensor analysis, and the finite element method would enhance the learning experience but are not necessary for studying with this textbook. The Finite Element Method is used as a tool to solve practical problems. For the most part, ANSYS is used throughout the book. Finite element programming is limited to programming material models, post processing algorithms, and so on. Basic knowledge of MATLAB is useful but not essential.
Only three software packages are used throughout the book. ANSYS is needed for Finite Element solution of numerous examples and suggested problems. MATLAB is needed for both symbolic and numerical solution of numerous examples and suggested problems. Additionally, BMI3™, which is available free of charge in the book's web site, is used in Chapter 4. Several other programs are also mentioned, such as ABAQUS™ and LS-DYNA™, but they are not used in the examples. All the code printed in the examples is available in the book's web site /feacm/.
Composite materials are now ubiquitous in the marketplace, including extensive applications in aerospace, automotive, civil infrastructure, sporting goods, and so on. Their design is especially challenging because, unlike conventional materials such as metals, the composite material itself is designed concurrently with the composite structure. Preliminary design of composites is based on the assumption of a state of plane stress in the laminate. Furthermore, rough approximations are made about the geometry of the part, as well as the loading and support conditions. In this way, relatively simple analysis methods exist and computations can be carried out simply using algebra. However, preliminary analysis methods have a number of shortcomings that are remedied with advanced mechanics and finite element analysis, as explained in this textbook.
Recent advances in commercial finite element analysis packages, with user friendly pre- and post-processing, as well as powerful user-programmable features, have made detailed analysis of composites quite accessible to the designer. This textbook bridges the gap between powerful finite element tools and practical problems in structural analysis of composites. I expect that many graduate students, practicing engineers, and instructors will find this to be a useful and practical textbook on finite element analysis of composite materials based on sound understanding of advanced mechanics of composite materials.
Ever J. Barbero, 2007