Finite Elements: An Introduction. Volume I

✍ Scribed by J. Tinsley Oden, Eric B. Becker, Graham F. Carey

• Publisher: Prentice Hall
• Year: 1981
• Tongue: English
• Leaves: 272
• Edition: 6th Printing
• Category: Library

✦ Synopsis

Finite elements book, like new

✦ Table of Contents

Cover
Title
CONTENTS
Preface
The Texas finite element series
1. A Model Problem
1.1 Orientation
1.2 The Statement of the Model Problem
1.3 Variational Statement of the Problem
1.3.1 A symmetric variational formulation
1.4 Galerkin Approximations
1.5 Finite Element Basis Functions
1.6 Finite Element Calculations
1.7 Interpretation of the Approximate Solution
1.8 Accuracy of the Finite Element Approximation
2. One-Dimensional Problems
2.1 Introduction
2.2 Classical Statements of Second-Order, Two-Point Boundary-Value Problems
2.2.1 Linear second-order problems
2.2.2 Physical origins of two-point problems
2.3 Variational Formulation of Two-Point Boundary-Value Problems
2.4 Galerkin Approximations
2.5 Minimization of Energy Functional
2.6 Finite Element Interpolation
2.7 Finite Element Approximation
2.7.1 Partitioning Q, and selection of shape functions
2.7.2 Calculation of element matrices and equations
2.7.3 Element assembly
2.7.4 Boundary conditions
2.7.5 Error estimates
3. Development of a Finite Element Program
3.1 Computer Implementation of the Finite Element Method
3.2 Description of CODE 1
3.3 Element Calculations
3.3.1 Integration rule—SETINT
3.3.2 Shape-function routine—SHAPE
3.3.3 Element routine—ELEM
3.3.4 Material-property routine—GETMAT
3.4 Preprocessing Routines
3.4.1 Preprocessor calling routine—PREP
3.4.2 Control data: routine—RCON
3.4.3 Nodal-point coordinate definition: routine — RNODE
3.4.4 Element data definition: routine—RELEM
3.4.5 Material-property definition: routine—RMAT
3.4.6 Boundary-condition definition: routine—RBC
3.5 Finite Element Calculation Routines
3.5.1 Processor calling: routine—PROC
3.5.2 Formulation of K and F; routine—FORMKF
3.5.3 Assembly routine—ASSMB
3.5.4 Boundary conditions: routine—APLYBC
3.5.5 Essential boundary condition: routine — DRCHLT
3.5.6 Equation solving: routine—SOLVE
3.5.7 Reduction ofK to triangular form: routine — TRI
3.5.8 Forward elimination ofF and calculation ofu: routine— RHSUB
3.6 Postprocessing
3.6.1 Postprocessing control: routine—POST
3.6.2 Evaluation of finite element and exact solutions: routine— EVAL
3.6.3 Error-norm calculation: routine—EN0RMS
3.6.4 Calculation of exact solution: routine—EXACT
3.7 Remarks on the Development of CODE1
3.8 Extension and Application of CODE1
3.8.1 Topics in code development
3.8.2 Numerical experiments
3.8.3 Applications using CODE1
4. Two-Dimensional Problems
4.1 Introduction
4.2 Two-Dimensional Boundary-Value Problems
4.2.1 Some preliminaries
4.2.2 Physical principles
4.2.3 Statement of the boundary-value problem
4.3 Variational Boundary-Value Problems
4.4 Finite Element Interpolation
4.4.1 Discretization
4.4.2 Piecewise-linear interpolation on triangles
4.4.3 Other triangular elements
4.4.4 Rectangular elements
4.4.5 Interpolation error
4.5 Finite Element Approximations
4.5.1 Approximation of two-dimensional boundary-value problems
4.5.2 An example
5. Two-Dimensional Element Calculations
5.1 Introduction
5.2 Element Transformations
5.2.1 The master element
5.2.2 Construction of the transformations Te
5.3 Finite Element Calculations
5.3.1 Master-element calculations
5.3.2 Computational aspects
5.4 Two-Dimensional Finite Elements
5.4.1 Quadrilateral elements
5.4.2 Triangular elements
5.5 Coding of Two-Dimensional Finite Element Calculations
5.5.1 Description of CODE2
5.5.2 Data storage in CODE2
5.5.3 Preprocessor routines
5.5.4 Processor routines
5.5.5 Postprocessor
6. Extensions
6.1 Introduction
6.2 Three-Dimensional Problems
6.3 Fourth-Order Problems
6.3.
6.3.2 Finite element approximations
6.3.3 A two-dimensional problem
6.4 Systems of Differential Equations
6.4.1 A one-dimensional system
6.4.2 Plane-stress problems
6.5 Time-Dependent Problems
Index