Fuzzy Randomness

Uncertainty in Civil Engineering and Computational Mechanics
2004
ISBN: 978-3-540-40294-7
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 336 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 694 g

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 stochastic 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 stochastic and nonstochastic 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 Stochastic Finite Element Method (FSFEM).

Zielgruppe

Professional/practitioner

Autoren/Hrsg.

Beer, Michael

Möller, Bernd

Fachgebiete

• Naturwissenschaften Physik Mechanik Klassische Mechanik, Newtonsche Mechanik
• Mathematik | Informatik Mathematik Stochastik Elementare Stochastik
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Technische Wissenschaften Bauingenieurwesen Mathematische Methoden, Computeranwendungen (Bauingenieurwesen)

Inhaltsverzeichnis

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 Stochastic Structural Analysis.- 6 Fuzzy Probabilistic Safety Assessment.- 7 Structural Design Based on Clustering.- References.

Über Autor(innen)

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.