The Finite Element Method

Fundamentals and Applications

Douglas H. Norrie, Gerard de Vries

• Publisher: Academic Press
• Year: 2014
• ISBN:
  9781483218915
• Topic: Technology & Engineering
• Subtopic: Civil Engineering
• Index: Technology & Engineering

The Finite Element Method: Fundamentals and Applications demonstrates the generality of the finite element method by providing a unified treatment of fundamentals and a broad coverage of applications. Topics covered include field problems and their approximate solutions; the variational method based on the Hilbert space; and the Ritz finite element method. Finite element applications in solid and structural mechanics are also discussed. Comprised of 16 chapters, this book begins with an introduction to the formulation and classification of physical problems, followed by a review of field or continuum problems and their approximate solutions by the method of trial functions. It is shown that the finite element method is a subclass of the method of trial functions and that a finite element formulation can, in principle, be developed for most trial function procedures. Variational and residual trial function methods are considered in some detail and their convergence is examined. After discussing the calculus of variations, both in classical and Hilbert space form, the fundamentals of the finite element method are analyzed. The variational approach is illustrated by outlining the Ritz finite element method. The application of the finite element method to solid and structural mechanics is also considered. This monograph will appeal to undergraduate and graduate students, engineers, scientists, and applied mathematicians.

Table of contents

• Front Cover
• The Finite Element Method
• Copyright Page
• Table of Contents
• Dedication
• PREFACE
• ACKNOWLEDGMENTS
• Chapter 1. The Formulation of Physical Problems
• Chapter 2. Field Problems and Their Approximate Solutions
• Chapter 3. The Variational Calculus and Its Application
• Chapter 4. The Variational Method Based on the Hilbert Space
• Chapter 5. Fundamentals of the Finite Element Approach
• Chapter 6. The Ritz Finite Element Method (Classical)
• Chapter 7. The Ritz Finite Element Method (Hilbert Space)
• Chapter 8. Finite Element Applications in Solid and Structural Mechanics
• Chapter 9. The Laplace or Potential Field
• Chapter 10. Laplace and Associated Boundary-Value Problems
• Chapter 11. The Helmholtz and Wave Equations
• Chapter 12. The Diffusion Equation
• Chapter 13. Finite Element Applications to Viscous Flow
• Chapter 14. Finite Element Applications to Compressible Flow
• Chapter 15. Finite Element Applications to More General Fluid Flows
• Chapter 16. Other Finite Element Applications
• Appendix A. Matrix Algebra
• Appendix B. The Differential and Integral Calculus of Matrices
• Appendix C. The Transformation Matrix
• Additional References
• AUTHOR INDEX
• SUBJECT INDEX