The Mathematics of Finite Elements and Applications

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

1st Edition - January 28, 1973

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  • Editor: J. R. Whiteman
  • eBook ISBN: 9781483268842

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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.

Table of Contents

  • Contributors


    Finite Elements-The Background Story

    An Introduction to the Mathematics of the Finite Element Method

    Some Recent Advances in the Mathematics of Finite Elements

    Error Analysis of Finite Element Methods With Triangles for Elliptic Boundary Value Problems

    Orders of Convergence in Finite Element Methods

    Finite Elements with Harmonic Interpolation Functions

    Variational Finite Element Methods for Initial Value Problems

    A Least Squares Finite Element Solution of Nonlinear Operators

    The l2 and l∞ Condition Numbers of the Finite Element Stiffness and Mass Matrices, and the Pointwise Convergence of the Method

    Dual Formulations for Potential and Complementary Energies. Unilateral Boundary Conditions. Applications to the Finite Element Method

    Generalised Matrix Inverse Techniques for Local Approximations of Operator Equations

    Finite Element Solution of Unsteady and Unsaturated Flow in Porous Media

    Sufficient Conditions for Convergence in the Finite Element Method for Any Solution of Finite Energy

    Combined Application of Finite Element Methods and Richardson Extrapolation to the Torsion Problem

    Finite Element Applications in Mathematical Physics

    A Dynamic Elastoplastic Analysis of Thin Shells of Revolution Under Asymmetric Mechanical and Thermal Loading

    On Hybrid Finite Elements

    Some Free Surface Transient Flow Problems of Seepage and Irrotational Flow

    Calculation of Stress Intensity Factors at Crack Tips Using Special Finite Elements

    Singularities in Transmission Lines

    Application of the Finite Element Method to the Extensional Vibrations of Piezoelectric Plates

    Vibration of Curved Structures Using Quadrilateral Finite Elements

    Assessment of Accuracies of Finite Element Eigenvalues

    Flexibility and Stiffness Matrices for an Open-Tube Warping Constraint Finite Element

    A Sandwich Plate Finite Element

    Application of Three-Dimensional Finite Elements for Analysis of Irradiation-Induced Stresses in Nuclear Reactor Fuel Elements

    The Analysis and Application of Sparse Matrix Algorithms in the Finite Element Method

    The Comparison of Iterative and Direct Solution Techniques in the Analysis of Time-Dependent Stress Problems, Including Creep

    A Method for Simulating Concentrated Forces and Local Reinforcements in Stress Computation

    Some Practical Solution Techniques for Finite Element Analysis

    Algorithm for the Large Deflection Geometrically Nonlinear Plane and Curved Structures

    Automated Solutions of Time Dependent Problems

Product details

  • No. of pages: 534
  • Language: English
  • Copyright: © Academic Press 1973
  • Published: January 28, 1973
  • Imprint: Academic Press
  • eBook ISBN: 9781483268842

About the Editor

J. R. Whiteman

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