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TU Dresden
Fakultät Bauingenieurwesen
Institut für Statik und Dynamik der Tragwerke
Prof. Dr.-Ing. habil. B. Möller
01062 Dresden
Germany

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M Liebscher and B Möller (2005)

Design of structures - solving the inverse problem

In: Compilation of Abstracts of the Third M.I.T. Conference Computational Fluid and Solid Mechanics, edited by K. J. Bathe. M.I.T., Boston, pages 233.

The presentation deals with the solution of the design problem as an inverse problem to nonlinear structural analysis. Starting point is the given point-to-point mapping between discrete points in the space of the design parameters (input parameters) and in the space of the constrained parameters (result parameters). These spaces are formed by input and result parameters, respectively, which are modeled as fuzzy sets. The point-to-point mapping results from the fuzzy probabilistic structural analysis or the fuzzy structural analysis. By comparing requirements regarding structural responses with the fuzzy results, points in the space of fuzzy design parameters are separated in a permissible and a non permissible set. Permissible points in the space of the fuzzy design parameters are determined. Permissible points in the space of design parameters are lumped together in clusters by applying crisp cluster methods or fuzzy cluster methods. The detected permissible clusters represent alternative structural design variants. The crisp values of structural responses are computed by applying defuzzification methods. In the presented study the centroid method and the defuzzification algorithms after Chen and Jain are proposed. The distance between the defuzzified result and the design constraints serve as an assessment criterion. Further, a second criterion is introduced as a robustness measure. The uncertainty of the fuzzy results and of the fuzzy design parameters is assessed on the basis of an analogon to Shannon´s entropy. As the robustness cannot be measured in absolute terms a relative sensitivity measure is formulated. If the uncertainty of the fuzzy results takes low values in relation to the uncertainty of the fuzzy input values, the associated structural design is then considered as being robust. In conclusion, the developed concept for uncertain structural design permits designing a structure on the basis of an arbitrary nonlinear fuzzy tructural analysis and fuzzy probabilistic structural analysis and additionally takes account of uncertainty. For the first time this concept provides a capable tool for determining permissible uncertain structural parameters and for assessing fuzzy input and fuzzy result values. The authors gratefully acknowledge the support of the German Research Foundation (DFG).
 
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Last modified 2006-12-04 10:24 AM
 

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