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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 86
Edited by: B.H.V. Topping
Paper 91

A Solution Method for Large Problems with Fuzzy Parameters

P. Štemberk1 and J. Kruis2

1Department of Concrete and Masonry Structures,
2Department of Mechanics,
Faculty of Civil Engineering, Czech Technical University in Prague, Czech Republic

Full Bibliographic Reference for this paper
P. Štemberk, J. Kruis, "A Solution Method for Large Problems with Fuzzy Parameters", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 91, 2007. doi:10.4203/ccp.86.91
Keywords: fuzzy numbers, fuzzy set theory, method of solution, parallelization, structural analysis.

The uncertainty contained in civil engineering problems can be dealt with using various tools. The established one is the probabilistic approach which is also the basis for reliability assessment of structures. For those problems which are difficult to define precisely, either due to limited knowledge or its complete absence, the fuzzy set approach can be utilized.

At previous conferences, the authors presented studies which focused on derivation of methods for analysis of civil engineering problems, such as fuzzy thermal analysis of a concrete wall subjected to thermal shock [1], and dynamically loaded frame structures with fuzzy input parameters [2,3]. It has been shown in the examples that the methods presented provided results where the fuzzy distribution reflected the fuzzy distribution of the input parameters at low computational cost, however, all examples were limited to relatively small finite element problems with the number of unknowns not exceeding two hundred. But, the real-life problems require tens of thousands of finite elements and unknowns for sufficient description.

This paper focuses on establishing a strategy for solution of large problems with the number of unknowns in orders of tens of thousands, which contrasts with the majority of recently published strategies, where feasibility of the approaches presented was proved using only very simple structures hardly resembling real industrial problems.

The proposed method makes use of the brute computational force available, which helps bypass the limitations stemming from the optimization-based solution strategies, and thus is quite robust. The advantage of this method is that the finite element codes developed for deterministic analyses can be used without any substantial modification. Moreover, the independent deterministic analyses can be also paralellized [4]. The fuzzy results are obtained by mere addition of the pre-processor, which prepares all relevant combination of values of input parameters and the post-processor, which sorts the results of the independent deterministic runs. The applicability of this method is limited only with the computational power which the designer has at hand.

The effectiveness of the method is shown in an example of fuzzy dynamic analysis of a multi-storey three-dimensional structure.

Štemberk, P. and Bittnar, Z., "Fuzzy Model of Heat Transfer", Computational Concrete Structures Technology, Civil-Comp Press, Edinburgh, UK, 119-124, 2000. doi:10.4203/ccp.69.4.1
Štemberk, P. and Kruis, J., "Fuzzy Dynamic Structural Analysis of 2D Frames", Proc. of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing, Civil-Comp Press, Stirling, UK, 2005. doi:10.4203/ccp.81.225
Štemberk, P. and Kruis, J., "Seismic Response of Structures with Uncertain Parameters", Proc. of the Eight International Conference on Computational Structures Technology, Civil-Comp Press, Stirling, UK, 2006. doi:10.4203/ccp.83.256
Kruis, J., "Domain Decomposition Methods for Distributed Computing", Saxe-Coburg Publications, Stirling, UK, 2006.

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