Fuzzy finite

Structural dynamics design validation and optimisation of structures with imprecise parameters using the fuzzy finite element method... 

ABSTRACT After initial research in the field of fuzzy finite elements has started in the middle of the nineties, different aspects of the problem have been considered, and continuous development has improved not only the capabilities but also the performance of the procedures. The improvement of the performance of fuzzy finite element analysis is still a big challenge. Vertex analysis with uncertain parameters requires 2 deterministic analysis runs for each a-level that is considered. Another approach is optimisation, which is capable of predicting absolute maxima and minima. Unlike vertex analysis, the performance of optimisation procedures is unpredictable. There is a strong demand to reduce the computation time. 

Structural dynamics is a specific type of problem that can also be tackled with interval or fuzzy finite elements. There is currently no generally applicable consistent approach to take into account the effect of parameter uncertainties on CMS reduction schemes. Some approximation procedures have been proposed, but they are sensitive to the particular case that is considered. 

The fuzzy finite element method (FFEM) has become a most valuable tool for the analysis of structural dynamics problems with imprecise parameters. The present paper gives an overview of the status of development of the FFEM. The paper focuses specifically on the capabilities of the method, especially in early stages of design analysis. The formulation of design criteria in the presence of parameter uncertainties is reviewed and options for early design optimisation are discussed. 

The second section deals with the analysis methods that are used in fuzzy finite element analysis. An overview of different approaches is presented first the transformation method, affine analysis, and global optimisation. The application to dynamic analysis is considered. The core of this section is the presentation of a consistent analysis approach to predict the effect of parameter uncertainties on different characteristics of dynamic behaviour of structures, resonance frequencies and dynamic response levels. A hybrid approach is developed, based on modal superposition and optimisation. 

Structural dynamics using fuzzy finite element method 87... 

This paper gives an overview of the current state of development of the fuzzy finite element method for dynamic analysis. After a review of definitions and generic analysis... 

The first improvement uses a Response Surface Methodology to reduce the calculation time. It takes advantage of the special properties of the optimisation problems. The result is a highly efficient procedure for interval and especially fuzzy finite element... 

De Gersem, H., Moens, D., Desmet, W. Vandepitte, D. 1005. A fuzzy finite element procedure for the calculation of uncertain frequency response functions of damped structures Part II -numerical case studies. Journal of Sound and Vibration, 288(3) 463—486. 

Rao, S. Sawyer, P. 1995. Fuzzy Finite Element Approach for the Analysis of Imprecisely Defined Systems, AIAA Journal, Vol. 33, No. 12, pp. 2364—2370. 

The theme of the contribution by Moens, Vandepitte, DeGersem, DeMunck and Desmet (Chapter 6) is structural dynamics design validation and optimization with imprecise parameters using the fuzzy finite element method. After initial research in the field of fuzzy finite elements has started in the middle of the nineties, different aspects... 

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