Affine Arithmetic Based Solution of Uncertain Static and Dynamic Problems

Uncertainty is an inseparable component of almost every measurement and occurrence when dealing with real-world problems. Finding solutions to real-life problems in an uncertain environment is a difficult and challenging task. As such, this book addresses the solution of uncertain static and dynamic problems based on affine arithmetic approaches. Affine arithmetic is one of the recent developments designed to handle such uncertainties in a different manner which may be useful for overcoming the dependency problem and may compute better enclosures of the solutions. Further, uncertain static and dynamic problems turn into interval and/or fuzzy linear/nonlinear systems of equations and eigenvalue problems, respectively. Accordingly, this book includes newly developed efficient methods to handle the said problems based on the affine and interval/fuzzy approach. Various illustrative examples concerning static and dynamic problems of structures have been investigated in order to showthe reliability and efficacy of the developed approaches.

Auteur

Dr. Snehashish Chakraverty works in the Department of Mathematics (Applied Mathematics Group), National Institute of Technology Rourkela, Odisha, as a Senior (Higher Administrative Grade) Professor and is also the Dean of Student Welfare of the institute since November 2019. He received his Ph.D. from IIT Roorkee in 1992. Then he did post-doctoral research at ISVR, University of Southampton, U.K., and at Concordia University, Canada. He was a visiting professor at Concordia and McGill Universities, Canada, and University of Johannesburg, South Africa. Prof. Chakraverty has authored 17 books and published approximately 345 research papers in journals and conferences. He was the President of the Section of Mathematical Sciences (including Statistics) of Indian Science Congress (2015-2016) and was the Vice President-Orissa Mathematical Society (2011-2013). Prof. Chakraverty is a recipient of prestigious awards viz. INSA International Bilateral Exchange Program, Platinum Jubilee ISCA Lecture, CSIR Young Scientist, BOYSCAST, UCOST Young Scientist, Golden Jubilee CBRI Director's Award, Roorkee University gold Medals and more. He has undertaken17 research projects as Principal Investigator funded by different agencies totaling about Rs.1.6 crores. Prof. Chakraverty is the Chief Editor of International Journal of Fuzzy Computation and Modelling (IJFCM), Inderscience Publisher, Switzerland, Associate Editor of Computational Methods in Structural Engineering, Frontiers in Built Environment, and an Editorial Board member of Springer Nature Applied Sciences, IGI Research Insights Books, Springer Book Series of Modeling and Optimization in Science andTechnologies, Coupled Systems Mechanics (Techno Press), Curved and Layered Structures (De Gruyter), Journal of Composites Science (MDPI), Engineering Research Express (IOP), Applications and Applied Mathematics: An International Journal, and Computational Engineering and Physical Modeling (Pouyan Press). His present research area includes Differential Equations (Ordinary, Partial, and Fractional), Numerical Analysis and Computational Methods, Structural Dynamics (FGM, Nano), and Fluid Dynamics, Mathematical Modeling and Uncertainty Modeling, and Soft Computing and Machine Intelligence (Artificial Neural Network, Fuzzy, Interval and Affine Computations).Saudamini Rout is currently pursuing her Ph.D. under the supervision of Prof. S. Chakraverty at the Department of Mathematics, National Institute of Technology Rourkela, Rourkela, Odisha, India. She completed her M.Phil. in Mathematics in 2016, M.Sc. in Mathematics in 2015, and B.Sc. in 2013 from Ravenshaw University, Cuttack, Odisha, India. She has been awarded a gold medal for securing first position in the university in M.Sc. She has been selected for the Biju Patnaik Research Fellowship, Department of Higher Education, Government of Odisha, India. She has participated in various conferences/workshops and published a few research articles and book chapters. She has also served as a reviewer for various international journals. Her current research interests include Fuzzy Set Theory, Interval Analysis, Affine Arithmetic, Uncertain Linear and/or Nonlinear Static and Dynamic Problems, and Numerical Analysis.

Contenu
Preface.- Acknowledgments.- Introduction.- Preliminaries.- Affine Arithmetic.- Fuzzy-Affine Arithmetic.- Uncertain Static Problems.- Uncertain Linear Dynamic Problems.- Uncertain Nonlinear Dynamic Problems.- Authors' Biographies.