Introductory Finite Element Method

✍ Scribed by Chandrakant S. Desai, Tribikram Kundu

• Publisher: CRC Press
• Year: 2001
• Tongue: English
• Leaves: 519
• Series: Mechanical and Aerospace Engineering Series
• Edition: 1
• Category: Library

✦ Synopsis

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

Content: 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

✦ Subjects

Éléments finis, Méthode des.;Analyse -- Application -- Calcul -- Chaleur -- Contrainte -- Deformation -- Ecoulement -- Element -- Fem -- Fini;Fluide -- Genie -- Ingenierie -- Mathematique -- Methode -- Resistance