Interval Finite Element Method with MATLAB

Interval Finite Element Method with MATLAB

by Sukanta Nayak, Snehashish Chakraverty
Released January 2018
Publisher(s): Academic Press
ISBN: 9780128129746

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Book description

Interval Finite Element Method with MATLAB provides a thorough introduction to an effective way of investigating problems involving uncertainty using computational modeling. The well-known and versatile Finite Element Method (FEM) is combined with the concept of interval uncertainties to develop the Interval Finite Element Method (IFEM). An interval or stochastic environment in parameters and variables is used in place of crisp ones to make the governing equations interval, thereby allowing modeling of the problem. The concept of interval uncertainties is systematically explained. Several examples are explored with IFEM using MATLAB on topics like spring mass, bar, truss and frame.

  • Provides a systematic approach to understanding the interval uncertainties caused by vague or imprecise data
  • Describes the interval finite element method in detail
  • Gives step-by-step instructions for how to use MATLAB code for IFEM
  • Provides a range of examples of IFEM in use, with accompanying MATLAB codes

Table of contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Copyright
  5. Author Biographies
  6. Preface
  7. Acknowledgments
  8. Chapter 1: Interval Arithematic
    1. Abstract
    2. 1.1 Truncation Error
    3. 1.2 Round-Off Error
    4. 1.3 Degenerate Intervals
    5. 1.4 Intersection, Union, and Interval Hull
    6. 1.5 Width, Absolute Value, Midpoint
    7. 1.6 Interval Arithmetic
  9. Chapter 2: Interval Finite Element Method
    1. Abstract
    2. 2.1 A Brief Overview
    3. 2.2 Finite Element Method (FEM)
    4. 2.3 Hybridization of Interval and Finite Element Method
  10. Chapter 3: Preliminaries of MATLAB®
    1. Abstract
    2. 3.1 Beginning With MATLAB®
    3. 3.2 Matrices, Operations, and Basic MATLAB® Functions
    4. 3.3 M-Files, Logical-Relational Operators, and IF Statements
    5. 3.4 Functions in MATLAB®
    6. 3.5 FOR and WHILE Loops in MATLAB®
    7. 3.6 Graphics in MATLAB®
    8. 3.7 Efficiency of Algorithms in MATLAB®
    9. 3.8 Useful Functions and Commands in MATLAB®
  11. Chapter 4: One-Dimensional Interval Finite Element
    1. Abstract
    2. 4.1 Spring Element
    3. 4.2 Linear Bar Element
    4. 4.3 Quadratic Bar Element
  12. Chapter 5: MATLAB® Code for One-Dimensional Interval Finite Element
    1. Abstract
    2. 5.1 MATLAB® Code for Spring Element
    3. 5.2 MATLAB® Code for Linear Bar Element
    4. 5.3 MATLAB® Code for Quadratic Bar Element
  13. Chapter 6: Two-Dimensional Interval Finite Element
    1. Abstract
    2. 6.1 Plane Truss Element
    3. 6.2 Beam Element
    4. 6.3 Plane Frame Element
    5. 6.4 Linear Triangular Element
  14. Chapter 7: MATLAB® Code for Two-Dimensional Interval Finite Element
    1. Abstract
    2. 7.1 MATLAB Code for Plane Truss Element
    3. 7.2 MATLAB® Code for Beam Element
    4. 7.3 MATLAB® Code for Plane Frame Element
    5. 7.4 MATLAB® Code for Linear Triangular Element
  15. Chapter 8: Three-Dimensional Interval Finite Element
    1. Abstract
    2. 8.1 Space Truss Element
    3. 8.2 Space Frame Element
    4. 8.3 Linear Tetrahedral Element
  16. Chapter 9: MATLAB® Code for Three-Dimensional Interval Finite Element
    1. Abstract
    2. 9.1 MATLAB® Code for Space Truss Element
    3. 9.2 MATLAB® Code for Space Frame Element
    4. 9.3 MATLAB® Code for Linear Tetrahedral Element
  17. Index

Product information

  • Title: Interval Finite Element Method with MATLAB
  • Author(s): Sukanta Nayak, Snehashish Chakraverty
  • Release date: January 2018
  • Publisher(s): Academic Press
  • ISBN: 9780128129746