Uncertain structural design based on nonlinear fuzzy analysis

In this paper a comprehensive application of fuzzy set theory in structural engineering is presented. Non-stochastic uncertainty is quantified using fuzzy values. The fuzzy structural parameters are processed on the basis of a generally applicable numerical method for arbitrary linear and nonlinear fuzzy structural analyses. This method is formulated in terms of α-level optimization combined with a modified evolution strategy. The fuzzy structural responses are compared with permissible values and assessed using an analog to the Shannon entropy and defuzzification algorithms. Referring to permissible fuzzy structural responses uncertain structural design parameters are derived by applying a fuzzy cluster analysis to the fuzzy structural parameters. The nonlinear fuzzy structural analysis including uncertain structural design is demonstrated by way of an example.

[1]  Joseph B. Kadane,et al.  Applying Non-parametric Robust Bayesian Analysis to Non-opiniated Judicial Neutrality , 2002, ISIPTA.

[2]  Andrea Bonarini,et al.  A qualitative simulation approach for fuzzy dynamical models , 1994, TOMC.

[3]  R. Grandhi,et al.  Efficient estimation of structural reliability for problems with uncertain intervals , 2002 .

[4]  I. Elishakoff,et al.  Convex models of uncertainty in applied mechanics , 1990 .

[5]  Z. Pawlak.  Rough Sets: Theoretical Aspects of Reasoning about Data , 1991 .

[6]  Volker Krätschmer,et al.  A unified approach to fuzzy random variables , 2001, Fuzzy Sets Syst..

[7]  G. Schuëller.  A state-of-the-art report on computational stochastic mechanics , 1997 .

[8]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[9]  V. J. Rayward-Smith,et al.  Fuzzy Cluster Analysis: Methods for Classification, Data Analysis and Image Recognition , 1999 .

[10]  Fulvio Tonon,et al.  A random set approach to the optimization of uncertain structures , 1998 .

[11]  Ahmed K. Noor,et al.  Uncertainty analysis of stiffened composite panels , 2001 .

[12]  F. Thouverez,et al.  ANALYSIS OF MECHANICAL SYSTEMS USING INTERVAL COMPUTATIONS APPLIED TO FINITE ELEMENT METHODS , 2001 .

[13]  Isaac Elishakoff,et al.  Whys and hows in uncertainty modelling : probability, fuzziness and anti-optimization , 1999 .

[14]  Li Bing,et al.  A practical engineering method for fuzzy reliability analysis of mechanical structures , 2000 .

[15]  Michael Oberguggenberger,et al.  Fuzzy Models in Geotechnical Engineering and Construction Management , 1999 .

[16]  Asce Bilal M. Ayyub Member.  GENERALIZED UNCERTAINTY IN STRUCTURAL RELIABILITY ASSESSMENT , 1994 .

[17]  Michael Hanss,et al.  The transformation method for the simulation and analysis of systems with uncertain parameters , 2002, Fuzzy Sets Syst..

[18]  K. Stange,et al.  Bayes-Verfahren : Schätz- und Testverfahren bei Berücksichtigung von Vorinformationen , 1977 .

[19]  W. Dong,et al.  Vertex method for computing functions of fuzzy variables , 1987 .

[20]  A. Muc,et al.  A fuzzy set analysis for a fracture and fatigue damage response of composite materials , 2001 .

[21]  Marco Savoia,et al.  Structural reliability analysis through fuzzy number approach, with application to stability , 2002 .