Introductory Finite Element Method

ISBN-13: 9780849302435 / Angielski / Twarda / 2001 / 520 str.

Chandrakant S. Desai; Tribikram Kundu; C. S. Desai

Opis

Written by authors who are well-known in the field of engineering, Int roductory Finite Element Method, an expanded version of the Elementary Finite Element Method published in 1979, represents the first work to deal with both structural analysis and flow problems at an elementary level. It not only appeals to undergraduate and beginning graduate en gineering students, but to those outside the field and practitioners a s well. Using this text, students will be able to form the functional and construct the element and global equations for a wide range of fie ld problems. It can easily be used as a primary textbook for a course taught in every university.

Recenzje

"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

Spis treści

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

O autorze

Desai, Chandrakant S.; Kundu, Tribikram