The Finite Element Method
eBook - PDF

The Finite Element Method

Fundamentals and Applications

  1. 336 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

The Finite Element Method

Fundamentals and Applications

About this book

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.

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Yes, you can access The Finite Element Method by Douglas H. Norrie,Gerard de Vries in PDF and/or ePUB format, as well as other popular books in Technology & Engineering & Mathematics General. We have over one million books available in our catalogue for you to explore.

Table of contents

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