The Finite Element Method: Its Basis and Fundamentals book cover

The Finite Element Method: Its Basis and Fundamentals

The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications.

This edition sees a significant rearrangement of the book’s content to enable clearer development of the finite element method, with major new chapters and sections added to cover:

  • Weak forms
  • Variational forms
  • Multi-dimensional field problems
  • Automatic mesh generation
  • Plate bending and shells
  • Developments in meshless techniques

Focusing on the core knowledge, mathematical and analytical tools needed for successful application, The Finite Element Method: Its Basis and Fundamentals is the authoritative resource of choice for graduate level students, researchers and professional engineers involved in finite element-based engineering analysis.

Mechanical, Civil and Electrical Engineers, applied mathematicians and computer aided engineering software developers

Hardbound, 756 Pages

Published: August 2013

Imprint: Butterworth Heinemann

ISBN: 978-1-85617-633-0


  • "...this is a book that you simply cannot afford to be without."--INTERNATIONAL JOURNAL OF NUMERICAL METHODS IN ENGINEERING


  • 1. The Standard Discrete System and Origins of the Finite Element Method
    2. Problems in Linear Elasticity and Fields
    3. Weak Forms and Finite Element Approximation: 1-D Problems
    4. Variational Forms and Finite Element Approximation: 1-D Problems
    5. Field Problems: A Multidimensional Finite Element Method
    6. Shape Functions, Derivatives, and Integration
    7. Elasticity: Two- and Three-Dimensional Finite Elements
    8. The Patch Test, Reduced Integration, and Nonconforming Elements
    9. Mixed Formulation and Constraints: Complete Field Methods
    10. Incompressible Problems, Mixed Methods and Other Procedures of Solution
    11. Multidomain Mixed Approximations
    12. The Time Dimension: Semi-Discretization of Field and Dynamic Problems
    13. Plate Bending Approximation: Thin and Thick Plates
    14. Shells as a Special Case of Three-Dimensional Analysis
    15. Errors, Recovery Processes, and Error Estimates
    16. Adaptive Finite Element Refinement
    17. Automative Mesh Generation
    18. Computer Procedures for Finite Element Analysis
    A. Matrix Algebra
    B. Some Vector Algebra
    C. Tensor-Indicial Notation in the Approximation of Elasticity Problems
    D. Solution of Simultaneous Linear Algebraic Equations
    E. Triangle and Tetrahedron Integrals
    F. Integration by Parts in Two or Three Dimensions (Green’s Theorem)
    G. Solutions Exact at Nodes
    H. Matrix Diagonalization or Lumping


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