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
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| Preface |
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| Acknowledgments |
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1 | (6) |
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2 | (1) |
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2 | (1) |
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3 | (1) |
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1.4 Intersection, Union, and Interval Hull |
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3 | (1) |
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1.5 Width, Absolute Value, Midpoint |
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3 | (1) |
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4 | (3) |
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5 | (2) |
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2 Interval Finite Element Method |
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7 | (12) |
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7 | (2) |
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2.2 Finite Element Method (FEM) |
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9 | (1) |
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2.3 Hybridization of Interval and Finite Element Method |
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10 | (9) |
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16 | (3) |
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3 Preliminaries of MATLAB® |
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19 | (16) |
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3.1 Beginning With MATLAB® |
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19 | (1) |
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3.2 Matrices, Operations, and Basic MATLAB® Functions |
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19 | (3) |
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3.3 M-Files, Logical-Relational Operators, and IF Statements |
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22 | (1) |
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23 | (1) |
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3.5 FOR and WHILE Loops in MATLAB® |
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23 | (2) |
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25 | (1) |
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3.7 Efficiency of Algorithms in MATLAB® |
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26 | (1) |
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3.8 Useful Functions and Commands in MATLAB® |
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26 | (9) |
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33 | (2) |
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4 One-Dimensional Interval Finite Element |
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35 | (12) |
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36 | (4) |
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40 | (3) |
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4.3 Quadratic Bar Element |
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43 | (4) |
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45 | (2) |
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5 MATLAB® Code for One-Dimensional Interval Finite Element |
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47 | (16) |
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5.1 MATLAB® Code for Spring Element |
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47 | (4) |
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5.2 MATLAB® Code for Linear Bar Element |
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51 | (4) |
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5.3 MATLAB® Code for Quadratic Bar Element |
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55 | (8) |
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61 | (2) |
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6 Two-Dimensional Interval Finite Element |
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63 | (16) |
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63 | (5) |
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68 | (3) |
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71 | (5) |
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6.4 Linear Triangular Element |
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76 | (3) |
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78 | (1) |
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7 MATLAB® Code for Two-Dimensional Interval Finite Element |
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79 | (26) |
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7.1 MATLAB Code for Plane Truss Element |
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79 | (7) |
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7.2 MATLAB® Code for Beam Element |
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86 | (4) |
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7.3 MATLAB® Code for Plane Frame Element |
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90 | (7) |
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7.4 MATLAB® Code for Linear Triangular Element |
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97 | (8) |
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104 | (1) |
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8 Three-Dimensional Interval Finite Element |
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105 | (14) |
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105 | (4) |
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109 | (5) |
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8.3 Linear Tetrahedral Element |
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114 | (5) |
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118 | (1) |
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9 MATLAB® Code for Three-Dimensional Interval Finite Element |
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119 | (32) |
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9.1 MATLAB® Code for Space Truss Element |
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119 | (7) |
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9.2 MATLAB® Code for Space Frame Element |
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126 | (12) |
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9.3 MATLAB® Code for Linear Tetrahedral Element |
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138 | (13) |
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150 | (1) |
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Dr Sukanta Nayak is Assistant Professor in the Department of Mathematics, at the Amrita School of Engineering in Coimbatore, India. He previously held a postdoctoral research fellowship at the University of Johannesburg, South Africa, and received his Ph.D. in mathematics from the National Institute of Technology Rourkela, in India. His research interests include numerical analysis, linear algebra, fuzzy finite element method, fuzzy heat, neutron diffusion equations, fuzzy stochastic differential equations and wavelet analysis. He has published widely in the field, including as co-author of a book entitled Interval Finite Element Method with MATLAB, for Elseviers Academic Press (2018). Dr. Snehashish Chakraverty is a Senior Professor in the Department of Mathematics (Applied Mathematics Group), National Institute of Technology Rourkela, with over 30 years of teaching and research experience. A gold medalist from the University of Roorkee (now IIT Roorkee), he earned his Ph.D. from IIT Roorkee and completed post-doctoral work at the University of Southampton (UK) and Concordia University (Canada). He has also served as a visiting professor in Canada and South Africa. Dr. Chakraverty has authored/edited 38 books and published over 495 research papers. His research spans differential equations (ordinary, partial, fractional), numerical and computational methods, structural and fluid dynamics, uncertainty modeling, and soft computing techniques. He has guided 27 Ph.D. scholars, with 10 currently under his supervision.
He has led 16 funded research projects and hosted international researchers through prestigious fellowships. Recognized in the top 2% of scientists globally (Stanford-Elsevier list, 20202024), he has received numerous awards including the CSIR Young Scientist Award, BOYSCAST Fellowship, INSA Bilateral Exchange, and IOP Top Cited Paper Awards. He is Chief Editor of International Journal of Fuzzy Computation and Modelling and serves on several international editorial boards.
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