Fuzzy Randomness: Uncertainty in Civil Engineering and Computational Mechanics

by Bernd Mïller, Michael Beer

Overview

sections dealing with fuzzy functions and fuzzy random functions are certain to be of special interest. The reader is expected to be in command of the knowledge gained in a basic university mathematics course, with the inclusion of shastic elements. A specification of uncertainty in any particular case is often difficult. For this reason Chaps. 3 and 4 are devoted solely to this problem. The derivation of fuzzy variables for representing informal and lexical uncertainty reflects the subjective assessment of objective conditions in the form of a membership function. Techniques for modeling fuzzy random variables are presented for data that simultaneously exhibit shastic and nonshastic properties. The application of fuzzy randomness is demonstrated in three fields of civil engineering and computational mechanics: structural analysis, safety assessment, and design. The methods of fuzzy structural analysis and fuzzy probabilistic structural analysis developed in Chap. 5 are applicable without restriction to arbitrary geometrically and physically nonlinear problems. The most important forms of the latter are the Fuzzy Finite Element Method (FFEM) and the Fuzzy Shastic Finite Element Method (FSFEM).

Product Details

ISBN-13:	9783540402947
Publisher:	Springer Berlin Heidelberg
Publication date:	03/31/2004
Series:	Engineering Online Library
Edition description:	2004
Pages:	336
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Univ.-Prof. Dr.-Ing. habil. Bernd MÖLLER (* 1941): studies in civil engineering (University of Technology, Dresden), main studies in constructional and structural engineering. Since 1996: Professor for Structural Analysis (University of Technology, Dresden).

Dr.-Ing. Michael BEER (* 1970): studies in civil engineering (University of Technology, Dresden), main studies in constructional and structural engineering. Since 2003: project manager of the DFG research project BE 2570/1 for funding the own occupation.

Table of Contents

1 Introduction.- 2 Mathematical Basics for the Formal Description of Uncertainty.- 3 Description of Uncertain Structural Parameters as Fuzzy Variables.- 4 Description of Uncertain Structural Parameters as Fuzzy Random Variables.- 5 Fuzzy and Fuzzy Shastic Structural Analysis.- 6 Fuzzy Probabilistic Safety Assessment.- 7 Structural Design Based on Clustering.- References.

Editorial Reviews

From the reviews:

"The subject of the book is the comprehensive consideration of uncertainty in the numerical analysis, the safety assessment, and the design of structures. … The book in particular is addressed to civil engineers … . But also for mechanical engineers … the book represents a suitable introduction to the problem of uncertainty modeling … . can be instrumental in broadening the interests and background of those who turn to it. The book demonstrates how one goes about taking account of uncertainty modeling and uncertainty models." (Current Engineering Practice – online, Vol. 47, 2004/2005)

"The book deals with a new and important subject of mathematical modeling in engineering, i.e. uncertainty models in civil engineering. It contains seven chapters and an extensive reference list. This work is recommended to engineers and scientists in the area of civil engineering, fuzzy analysis and the corresponding numerical methods." (Olivian Simionescu, Zentralblatt MATH, Vol. 1080, 2006)

"To my best knowledge, this is the first book that covers fuzzy randomness in a comprehensive way. The motivation of the authors to study fuzzy randomness was to deal with some difficult problems in the field of civil engineering and computational mechanics in a more realistic fashion. … this is an important book. I have no doubt that it will stimulate the use of fuzzy randomness not only in civil engineering and computational mechanics, but in other areas as well." (George J. Klir, International Journal of General Systems, Vol. 34 (3), 2005)

From the Publisher