Finite element procedures for solids and structures : nonlinear analysis

Preface Finite element procedures are now an important and frequently indispensable part of engineering analysis and design. Finite element computer programs are now widely used in practically all branches of engineering for the analysis of structures, solids, and fluids. My objective in writing this book was to provide a text for upper-level undergraduate and graduate courses on finite element analysis and to provide a book for self-study by engineers and scientists. With this objective in mind, I have developed this book from my earlier publication Finite Element Procedures in Engineering Analysis (Prentice-Hall, 1982). I have kept the same mode of presentation but have consolidated, updated, and strengthened the earlier writing to the current state of finite element developments. Also, I have added new sections, both to cover some important additional topics for completeness of the presentation and to facilitate (through exercises) the teaching of the material discussed in the book. This text does not present a survey of finite element methods. For such an endeavor, anumber of volumes would be needed. Instead, this book concentrates only on certain finite element procedures, namely, on techniques that I consider very useful in engineering practice and that will probably be employed for many years to come. Also, these methods are introduced in such a way that they can be taught effectively—and in an exciting manner—to students. An important aspect of a finite element procedure is its reliability, so that the method can be used in a confident manner in computer-aided design. This book emphasizes this point throughout the presentations and concentrates on finite element procedures that are general and reliable for engineering analysis. Hence, this book is clearly biased in that it presents only certain finite element procedures and in that it presents these procedures in a certain manner. In this regard, the book reflects my philosophy toward the teaching and the use of finite element methods. While the basic topics of this book focus on mathematical methods, an exciting and thorough understanding of finite element procedures for engineering applications is achieved only if sufficient attention is given to both the physical and mathematical charac- teristics of the procedures. The combined physical and mathematical understanding greatly enriches our confident use and further development of finite element methods and is there- fore emphasized in this text. These thoughts also indicate that a collaborauon between engineers and mathemati- cians to deepen our understanding of finite element methods and to further advance in the fields of research can be of great benefit. Indeed, I am thankful to the mathematician Franco Brezzi for our research collaboration in this spirit, and for his valuable suggestions regard- ing this book. I consider it one of the greatest achievements for an educator to write a valuable book. In these times, all fields of engineering are rapidly changing, and new books for students are needed in practically all areas of engineering. I am therefore grateful that the Mechanical Engineering Department of M.L.T. has provided me with an excellent environment in which. to pursue my interests in teaching, research, and scholarly writing. While it required an immense effort on my part to write this book, I wanted to accomplish this task as a commitment to my past and future students, to any educators and researchers who might have an interest in the work, and, of course, to improve upon my teaching at M.I.T. I have been truly fortunate to work with many outstanding students at M.I.T., for which I am very thankful. It has been a great privilege to be their teacher and work with them. Of much value has also been that I have been intimately involved, at my company ADINA R & D, Inc., in the development of finite element methods for industry. This involvement has been very beneficial in my teaching and research, and in my writing of this book. A text of significant depth and breadth on a subject that came to life only a few decades ago and that has experienced tremendous advances, can be written only by an author who has had the benefit of interacting with many people in the field. I would like to thank all my students and friends who contributed—and will continue to contribute—to my knowledge and understanding of finite element methods. My interaction with them has given me great joy and satisfaction. I also would like to thank my secretary, Kristan Raymond, for her special efforts in typing the manuscript of this text. Finally, truly unbounded thanks are due to my wife, Zorka, and children, Ingrid and Mark, who, with their love and their understanding of my efforts, supported me in writing this book. K. J. Bathe Ch. 1. An Introduction To The Use Of Finite Element Procedures -- Ch. 2. Vectors, Matrices, And Tensors -- Ch. 3. Some Basic Concepts Of Engineering Analysis And An Introduction To The Finite Element Method -- Ch. 4. Formulation Of The Finite Element Method -- Linear Analysis In Solid And Structural Mechanics -- Ch. 5. Formulation And Calculation Of Isoparametric Finite Element Matrices -- Ch. 6. Finite Element Nonlinear Analysis In Solid And Structural Mechanics -- Ch. 7. Finite Element Analysis Of Heat Transfer, Field Problems, And Incompressible Fluid Flows -- Ch. 8. Solution Of Equilibrium Equations In Static Analysis -- Ch. 9. Solution Of Equilibrium Equations In Dynamic Analysis -- Ch. 10. Preliminaries To The Solution Of Eigenproblems -- Ch. 11. Solution Methods For Eigenproblems -- Ch. 12. Implementation Of The Finite Element Method. Klaus-jürgen Bathe. Revision Of: Finite Element Procedures In Engineering Analysis. 1982. Includes Bibliographical References (p. 1013-1028) And Index. For courses in finite element methods, finite element analysis taught in departments of Civil, Mechanical, Aerospace, Agriculture, and Mechanics departments. Course for which this book is appropriate is usually taught to seniors or graduate students.Comprehensive -- this text explores the full range of finite element methods used in engineering practice for actual applications in computer-aided design. It provides not only an introduction to finite element methods and the commonality in the various techniques, but explores state-of-the-art methods as well -- with a focus on what are deemed to become "classical techniques" -- procedures that will be standard and authoritative for finite element analysis for years to come. Revision of the 1982 classic. Covers finite element procedures in Engineering Analysis in Finite Element Methods. Bathe's strong inclination toward useful methods makes this book very practical. While mathematically sophisticated, the work builds its foundation on presenting procedures that work. Explores the range of finite element methods used in engineering practice for actual applications in computer-aided design. This book provides not only an introduction to finite element methods and the commonality in the various techniques, but also explores methods. This text explores the full range of infinite element methods used in engineering practice for actual applications in computer-aided design. It provides an introduction to finite element methods and the commonality in the various techniques.