Introductory Finite Element Method

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ISBN 9780849302435
Cat# 0618

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Features

  • Offers a simpler, unified introduction to applying the finite element method
  • Enables readers to construct the element and global equations for a wide range of field problems
  • Addresses both structural analysis and fluid/heat flow problems and clearly shows the similarities between the two
  • Explores both the variational method and Galerkin's method
  • Provides one- and two-dimensional finite element codes
  • Includes a wide range of examples and exercise problems
  • Summary

    Although there are many books on the finite element method (FEM) on the market, very few present its basic formulation in a simple, unified manner. Furthermore, many of the available texts address either only structure-related problems or only fluid or heat-flow problems, and those that explore both do so at an advanced level.

    Introductory Finite Element Method examines both structural analysis and flow (heat and fluid) applications in a presentation specifically designed for upper-level undergraduate and beginning graduate students, both within and outside of the engineering disciplines. It includes a chapter on variational calculus, clearly presented to show how the functionals for structural analysis and flow problems are formulated. The authors provide both one- and two-dimensional finite element codes and a wide range of examples and exercises. The exercises include some simpler ones to solve by hand calculation-this allows readers to understand the theory and assimilate the details of the steps in formulating computer implementations of the method.

    Anyone interested in learning to solve boundary value problems numerically deserves a straightforward and practical introduction to the powerful FEM. Its clear, simplified presentation and attention to both flow and structural problems make Introductory Finite Element Method the ideal gateway to using the FEM in a variety of applications.

    Table of Contents

    INTRODUCTION
    Basic Concept
    Process of Discretization
    Principles and Laws
    Cause and Effect
    Review Assignments
    STEPS IN THE FINITE ELEMENT METHOD
    Introduction
    General Idea
    Introduction to Variational Calculus
    Summary
    ONE-DIMENSIONAL STRESS DEFORMATION
    Introduction
    Explanation of Global and Local Coordinates
    Local and Global Coordinate System for the One-Dimensional Problem
    Interpolation Functions
    Relation Between Local and Global Coordinates
    Requirements for Approximation Functions
    Stress-Strain Relation
    Principle of Minimum Potential Energy
    Expansion of Terms
    Integration
    Direct Stiffness Method
    Boundary Conditions
    Strains and Stresses
    Formulation by Galerkin's Method
    Computer Implementation
    Other Procedures for Formulation
    Complementary Energy Approach
    Mixed Approach
    Bounds
    Advantages of the Finite Element Method
    ONE-DIMENSIONAL FLOW
    Theory and Formulation
    Problems
    Bibliography
    ONE-DIMENSIONAL TIME-DEPENDENT FLOW: Introduction to Uncoupled and Coupled Problems
    Uncoupled Case
    Time-Dependent Problems
    One-Dimensional Consolidation
    Computer Code
    FINITE ELEMENT CODES: ONE AND TWO-DIMENSIONAL PROBLEMS
    One-Dimensional Code
    Philosophy of Codes
    Stages
    Explanation of Major Symbols and Arrays
    User's Guide for Code DFT/C1DFE
    Two-Dimensional Code
    User's Guide for Plane-2D
    Sample Problems for Plane-2D
    User's Guide for Field-2D
    Sample Problems for Field-2D
    BEAM BENDING AND BEAM COLUMN
    Introduction
    Beam-Column
    Other Procedures for Formulation
    ONE-DIMENSIONAL MASS TRANSPORT
    Introduction
    Finite Element Formulation
    References
    Bibliography
    ONE-DIMENSIONAL STRESS WAVE PROPAGATION
    Introduction
    Finite Element Formulation
    Convection Parameter ux
    Bibliography
    TWO AND THREE DIMENSIONAL FORMULATIONS
    Introduction
    Two-Dimensional Formulation
    Three-Dimensional Formulation
    ONE-DIMENSIONAL STRESS WAVE PROPAGATION
    Introduction
    Finite Element Formulation
    Boundary and Initial Conditions
    Boundary Conditions
    TWO-AND THREE-DIMENSIONAL FORMULATIONS
    Introduction
    Two-Dimensional Formulation
    Triangular Element
    Quadrilateral Element
    Three-Dimensional Formulation
    Tetrahedron Element
    Brick Element
    TORSION
    Introduction
    Finite Element Formulation (Displacement Approach)
    Comparison of Numerical Predictions and Closed Form Solutions
    Stress Approach
    Review and Comments
    Hybrid Approach
    Mixed Approach
    Static Condensation
    OTHER FIELD PROBLEMS: POTENTIAL, THERMAL, FLUID, AND ELECTRICAL FLOW
    Introduction
    Potential Flow
    Finite Element Formulation
    Stream Function Formulation
    Thermal or Heat Flow Problem
    Seepage
    Electromagnetic Problems
    Computer Code
    TWO-DIMENSIONAL STRESS-DEFORMATION ANALYSIS
    Introduction
    Plane Deformations
    Finite Element Formulation
    Computer Code
    MULTICOMPONENT SYSTEMS: BUILDING FRAME AND FOUNDATION
    Introduction
    Various Components
    Computer Code
    Transformation of Coordinates
    APPENDIX 1: Various Numerical Procedures: Solution to Beam Bending Problem
    APPENDIX 2: Solution of Simultaneous Equations
    APPENDIX 3 Computer Codes

    Each chapter also contains sections of problems and references

    Editorial Reviews

    "This is an excellent addition to the available textbooks on finite element method…The mathematical formulations and fundamental concepts illustrated with simple examples and summaries or comments and plenty of exercises presented at the end of each chapter are other merits of the book…The book is highly recommended for undergraduate students and teachers in universities."
    - Appl Mech Rev, Vol. 55, no. 1

    "Intended for use… within and outside engineering disciplines, this book examines both stress-deformation analysis and flow (heat and fluid) applications…. offers an introduction to the finite element method…"
    -Sci Tech Book News, Vol. 25, No. 3, September 2001

    Downloads / Updates

    Resource OS Platform Updated Description Instructions
    0618.zip All Windows Version September 10, 2001