Fuzzy variational principle and its applications
Author(s)
Author(s)
Yang, L. F.
Li. Q. S.
Zhao, Y. L.
Li, G. Q.
Date Issued
2002
Publisher
Elsevier
Journal
European Journal of Mechanics - A/Solids
Volume
21
Issue
6
Start page
999
End page
1018
Abstract
Linear and non-linear peaky fuzzy numbers and their arithmetic operations are constructed for the analysis of engineering structures with fuzzy characteristic quantities. Fuzziness of the corresponding quantities is consistently incorporated into the functional of the total potential energy. A set of deterministic recursive equations is obtained as the alternative expressions of the fuzzy variational principle by means of the second-order perturbation technique. The fuzzy Ritz method and the fuzzy finite element method are presented as the applications of the fuzzy variational principle. Accordingly, the roundabout procedures frequently used in the formulations of the fuzzy finite element method are avoided. A benchmark problem of a bending beam with fuzzy Young's modulus under fuzzy external loading is solved by the developed fuzzy numerical methods. Numerical examples show that results determined by these two fuzzy methods are both little conservative, and are in good agreement with those obtained by the analytical method. Moreover, the fuzzy Ritz method or the fuzzy finite element method can provide more valuable information than the conventional deterministic methods.
SFU Affiliated Publication
No
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