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Introductory Finite Element Method




ISBN 9780849302435
Published May 18, 2001 by CRC Press
520 Pages - 200 B/W Illustrations

 
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Book Description

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

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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