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G.I. Schuëller Institute of Engineering Mechanics Leopold-Franzens University

Workshop on Application of Fuzzy Sets & Fuzzy Logic to Engineering Problems Introductory Remarks. G.I. Schuëller Institute of Engineering Mechanics Leopold-Franzens University Innsbruck , Austria, EU. Pertisau, Tyrol, Austria, EU Sept. 29 – Oct. 1, 2002. Mechanical Model. Physical.

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G.I. Schuëller Institute of Engineering Mechanics Leopold-Franzens University

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  1. Workshop onApplication of Fuzzy Sets & Fuzzy Logic to Engineering ProblemsIntroductory Remarks G.I. Schuëller Institute of Engineering Mechanics Leopold-Franzens University Innsbruck, Austria, EU Pertisau, Tyrol, Austria, EUSept. 29 – Oct. 1, 2002

  2. Mechanical Model Physical Entire Spectrum Spectrum of Uncertainties

  3. Spectrum of Uncertainties - Examples Wind (turbulence) Earthquake Materials (strength) Buckling loads Crack growth

  4. Evolution of Structural Mechanics • Deterministic approach • Stochastic approach • Adding additional information • Replace single point by distribution

  5. Advantages of Stochastic Analysis of Uncertainties • Quantification of Reliability possible • More realistic response evaluation • Adequate for environmental loading But: • Increase in information requires increase of computational efforts Resistance Stress Computational Efficiency is a key issue

  6. f(x1 ,x2 ) x2 x1 z x y Quantification of Randomness Random Variable Random ProcessesRandom Field Autocorrelation Function:

  7. Random Fields • Gaussian distributed • Spectral representation • Karhunen-Loéve expansion

  8. Damage Effects by Crack Propagation • Structural life • Crack growth is in reality a stochastic process • Deterministic modeling is just an approximation • Crack growth models: • Random variables • In general as SDE: R.V. R.V.

  9. Concepts to Assess Uncertainties Fuzzy Algorithm Bignoli et al.

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