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A Fuzzy Finite Element Method (FFEM) for the analysis of
imprecisely defined structures is being developed. The approach is
applicable to systems that are partially described in linguistic
terms or by incomplete information. It handles certain types of
imprecisely known data more realistically compared with the
existing probabilistic procedures. Furthermore, the fuzzy method
intends to substantially reduce the computational effort compared
to these probabilistic procedures.
The development of the methodology starts with the basic concept
of fuzzy numbers and fuzzy arithmetic. It implements fuzzy calculus
concepts for the derivation, manipulation and solution of the
finite element equations. However, the basic finite element scheme
remains unchanged.
Over the past 15 years, the research group has mainly focussed
on efficient solution strategies for the Fuzzy FE problem, based on
global optimisation strategies, response surface techniques and
substructuring methods. Throughout the research, specific emphasis
lies on the generic numerical implementation of the developed
algorithms. The fuzzy modelling strategies are being automated in
view of their use for larger industrial models by linking the code
to commercial FE solver codes, as e.g. Nastran.
The current research track focuses on the representation of
spatially dependent uncertainty. In most cases uncertainty in a
model cannot be described by a single uncertain parameter (for
example the thickness of a rolled plate). The introduction of
multiple uncertain parameters requires a sound mathematical
framework to represent their mutual dependencies. The dependencies
themselves are not as uncertain as the actual values of the
parameters. The research focuses on representing these dependent
uncertainties by two entities: an entity representing the (spatial)
dependency (a base vector) and an entity representing the
uncertainty itself (an interval factor). Research results from the
above mentioned substructuring techniques and optimisation methods
provide a start for respectively the base vector definition and the
method to find the bounds on the interval factors. Special
attention is given to the visualisation of the uncertainties on the
model both for the input and the output of a finite element
analysis. The applicability of the method is being tested through
different test cases.
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