The Mathematics of Finite Elements and Applications
eBook - PDF

The Mathematics of Finite Elements and Applications

Proceedings of the Brunel University Conference of the Institute of Mathematics and Its Applications Held in April 1972

  1. 534 pages
  2. English
  3. PDF
  4. Only available on web
eBook - PDF

The Mathematics of Finite Elements and Applications

Proceedings of the Brunel University Conference of the Institute of Mathematics and Its Applications Held in April 1972

Book details
Table of contents
Citations

About This Book

The Mathematics of Finite Elements and Applications provides information pertinent to the mathematics of finite elements, applications, algorithms, and computational techniques. This book discusses the developments in the mathematics of finite elements. Organized into 32 chapters, this book begins with an overview of the basis of the finite element process as a general approximation tool. This text then examines the methods for obtaining bounds on the errors in finite element solutions to two-dimensional elliptic boundary value problems defined on simply connected polygonal regions. Other chapters consider the practical implementation of the Galerkin and the Rayleigh–Ritz methods to equations of importance to physics and engineering. This book discusses as well a fundamental investigation into the problem of convergence in the finite element method. The final chapter deals with an algorithm that is applicable to the analysis of arbitrary plane stress or plane strain configurations. This book is a valuable resource for numerical analysts, mathematical physicist, applied mathematicians, computer scientists, and engineers.

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Information

Publisher
Academic Press
Year
2014
ISBN
9781483268842
Topic
Mathematics
Subtopic
Mathematical Analysis
Index
Mathematics

Table of contents

  1. Front Cover
  2. The Mathematics of Finite Elements and Applications
  3. Copyright Page
  4. Table of Contents
  5. Contributors
  6. Preface
  7. CHAPTER 1. FINITE ELEMENTS—THE BACKGROUND STORY
  8. CHAPTER 2. AN INTRODUCTION TO THE MATHEMATICS OF THE FINITE ELEMENT METHOD
  9. CHAPTER 3. SOME RECENT ADVANCES IN THE MATHEMATICS OF FINITE ELEMENTS
  10. CHAPTER 4. ERROR ANALYSIS OF FINITE ELEMENT METHODS WITH TRIANGLES FOR ELLIPTIC BOUNDARY VALUE PROBLEMS
  11. CHAPTER 5. ORDERS OF CONVERGENCE IN FINITE ELEMENT METHODS
  12. CHAPTER 6. FINITE ELEMENTS WITH HARMONIC INTERPOLATION FUNCTIONS
  13. CHAPTER 7. VARIATIONAL FINITE ELEMENT METHODS FOR INITIAL VALUE PROBLEMS
  14. CHAPTER 8. A LEAST SQUARES FINITE ELEMENT SOLUTION OF NONLINEAR OPERATORS
  15. CHAPTER 9. THE L2 AND L∞ CONDITION NUMBERS OF THE FINITE ELEMENT STIFFNESS AND MASS MATRICES, AND THE POINTWISE CONVERGENCE OF THE METHOD
  16. CHAPTER 10. DUAL FORMULATIONS FOR POTENTIAL AND COMPLEMENTARY ENERGIES. UNILATERAL BOUNDARY CONDITIONS. APPLICATIONS TO THE FINITE ELEMENT METHOD
  17. CHAPTER 11. GENERALISED MATRIX INVERSE TECHNIQUES FOR LOCAL APPROXIMATIONS OF OPERATOR EQUATIONS
  18. CHAPTER 12. FINITE ELEMENT SOLUTION OF UNSTEADY AND UNSATURATED FLOW IN POROUS MEDIA
  19. CHAPTER 13. SUFFICIENT CONDITIONS FOR CONVERGENCE IN THE FINITE ELEMENT METHOD FOR ANY SOLUTION OF FINITE ENERGY
  20. CHAPTER 14. COMBINED APPLICATION OF FINITE ELEMENT METHODS AND RICHARDSON EXTRAPOLATION TO THE TORSION PROBLEM
  21. CHAPTER 15. FINITE ELEMENT APPLICATIONS IN MATHEMATICAL PHYSICS
  22. CHAPTER 16. A DYNAMIC ELASTOPLASTIC ANALYSIS OF THIN SHELLS OF REVOLUTION UNDER ASYMMETRIC MECHANICAL AND THERMAL LOADING
  23. CHAPTER 17. ON HYBRID FINITE ELEMENTS
  24. CHAPTER 18. SOME FREE SURFACE TRANSIENT FLOW PROBLEMS OF SEEPAGE AND IRROTATIONAL FLOW
  25. CHAPTER 19. CALCULATION OF STRESS INTENSITY FACTORS AT CRACK TIPS USING SPECIAL FINITE ELEMENTS
  26. CHAPTER 20. SINGULARITIES IN TRANSMISSION LINES
  27. CHAPTER 21. APPLICATION OF THE FINITE ELEMENT METHOD TO THE EXTENSIONAL VIBRATIONS OF PIEZOELECTRIC PLATES
  28. CHAPTER 22. VIBRATION OF CURVED STRUCTURES USING QUADRILATERAL FINITE ELEMENTS
  29. CHAPTER 23. ASSESSMENT OF ACCURACIES OF FINITE ELEMENT EIGENVALUES
  30. CHAPTER 24. FLEXIBILITY AND STIFFNESS MATRICES FOR AN OPEN-TUBE WARPING CONSTRAINT FINITE ELEMENT
  31. CHAPTER 25. A SANDWICH PLATE FINITE ELEMENT
  32. CHAPTER 26. APPLICATION OF THREE-DIMENSIONAL FINITE ELEMENTS FOR ANALYSIS OF IRRADIATIONINDUCED STRESSES IN NUCLEAR REACTOR FUEL ELEMENTS
  33. CHAPTER 27. THE ANALYSIS AND APPLICATION OF SPARSE MATRIX ALGORITHMS IN THE FINITE ELEMENT METHOD
  34. CHAPTER 28. THE COMPARISON OF ITERATIVE AND DIRECT SOLUTION TECHNIQUES IN THE ANALYSIS OF TIME-DEPENDENT STRESS PROBLEMS, INCLUDING CREEP, BY THE FINITE ELEMENT METHOD
  35. CHAPTER 29. A METHOD FOR SIMULATING CONCENTRATED FORCES AND LOCAL REINFORCEMENTS IN STRESS COMPUTATION
  36. CHAPTER 30. SOME PRACTICAL SOLUTION TECHNIQUES FOR FINITE ELEMENT ANALYSIS
  37. CHAPTER 31. ALGORITHM FOR THE LARGE DEFLECTION GEOMETRICALLY NONLINEAR PLANE AND CURVED STRUCTURES
  38. CHAPTER 32. AUTOMATED SOLUTIONS OF TIME DEPENDENT PROBLEMS
  39. AUTHOR INDEX
  40. SUBJECT INDEX