×

Finite element analysis of flexible multibody systems with fuzzy parameters. (English) Zbl 0948.70004

Summary: We present a computational procedure for predicting the dynamic response and evaluating the sensitivity coefficients of flexible multibody systems whose characteristics include fuzzy parameters. Time-histories of the possibility distributions of the response and the sensitivity coefficients are generated. These coefficients measure the sensitivity of the dynamic response to variations in the material and in the geometric and external force parameters of the system. The five key components of the procedure are: a) a corotational frame approach used in conjunction with a total Lagrangian formulation; b) beam and shell elements with Cartesian coordinates of the nodes selected as degrees of freedom, and with continuous inter-element slopes; c) the use of an approximate method of extension, based on the \(\alpha\)-cut representation, called the ‘vertex method’ for generating the possibility distributions of the desired response quantities and their sensitivity coefficients; d) semi-explicit temporal integration technique for generating the dynamic response; and e) direct differentiation approach for evaluating the sensitivity coefficients. The effectiveness of the procedure and the usefulness of the fuzzy output are demonstrated through numerical examples, including an articulated space structure consisting of beams, shells and revolute joints.

MSC:

70-08 Computational methods for problems pertaining to mechanics of particles and systems
70E55 Dynamics of multibody systems
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Elishakoff, I., Essay on uncertainties in elastic and viscoelastic structures: From A.M. Freudenthal’s Criticism to modern convex modeling, Comput. Struct., 56, 6, 871-895 (1995) · Zbl 0921.73004
[2] Araujo, J. M.; Awruch, A. M., On stochastic finite elements for structural analysis, Comput. Struct., 52, 3, 461-469 (1994) · Zbl 0872.73058
[3] Kleiber, M.; Hien, T. D., The Stochastic Finite Element Method (1992), John Wiley: John Wiley New York · Zbl 0727.73098
[4] Chamis, C. C.; Hopkins, D. A., Probabilistic Structural Analysis Methods Program Overview, NASA CP-10064 (1991)
[5] Elishakoff, I., Convex versus probabilistic models of uncertainty in structural dynamics, opening keynote lecture, (Petyt, M.; Wolfe, H. F.; Mei, C., Structural Dynamics: Recent Advances (1990), Elsevier Applied Science: Elsevier Applied Science London), 3-21
[6] Kaufman, A.; Gupta, M. M., Introduction to Fuzzy Arithmetic: Theory and Applications (1985), Van Nostrand Reinhold Company, Inc: Van Nostrand Reinhold Company, Inc New York
[7] Ross, T., Fuzzy Logic with Engineering Applications (1995), McGraw-Hill: McGraw-Hill New York · Zbl 0855.93003
[8] Mares, M., Computation Over Fuzzy Quantities (1994), CRC Press: CRC Press Boca Raton, FL · Zbl 0859.94035
[9] Zhao, R.; Govind, R., Solution of algebraic equations involving generalized fuzzy numbers, Infor. Sci., 56, 1-3, 199-243 (1991) · Zbl 0726.65048
[10] Shen, Q.; Leitch, R., Fuzzy qualitative simulation, IEEE Transaction on Systems, Man, and Cybernetics, 23, 4, 1038-1061 (1993)
[11] James, P., Qualitative simulation of electrical and mechanical systems, Simulation, 63, 1, 48-58 (1994)
[12] Dong, W.; Shah, H.; Wong, F., Fuzzy computations in risk and decision analysis, Civil Engrg. Syst., 24, 65-78 (1985)
[13] Chao, R. J.; Ayyub, B. M., Fuzzy-based analysis of structures, (Proc. Third Int. Symp. on Uncertainty Modeling and Analysis and Annual Conference of the North American Fuzzy Information Processing Society (ISUMA-NAFIPS) (1995), IEEE Computer Society Press), 355-360
[14] Chao, R. J.; Ayyub, B. M., Finite element analysis with fuzzy variables, (Building an International Community of Structural Engineers, ASCE Structures Congress — Proceedings, 1 (1996)), 643-650
[15] Valliapan, S.; Pham, T. D., Fuzzy finite element analysis of a foundation on an elastic soil medium, Int. J. Numer. Analyt. Methods Geomech., 17, 11, 771-789 (1993) · Zbl 0800.73458
[16] Valliapan, S.; Pham, T. D., Elasto-plastic finite element analysis with fuzzy parameters, Inter. J. Numer. Methods Engrg., 38, 4, 531-548 (1995) · Zbl 0823.73073
[17] Pham, T. D., Modeling of a Fuzzy System in Geotechnical Engineering, (Proc. Third IEEE Conf. Fuzzy Syst. (1994)), 1861-1866, Orlando, FL · Zbl 1365.93442
[18] Pham, T. D.; Valliapan, S.; Yazdchi, M., Modeling of fuzzy damping in dynamic finite element analysis, (Proc. Fourth IEEE Inter. Conf. Fuzzy Syst. (1995)), 1971-1978, Yokohama, Japan
[19] Dong, W.; Shah, H., Vertex method for computing functions of fuzzy variables, Fuzzy Sets and Systems, 2, 201-208 (1987)
[20] Lamego, M. M.; Rey, J. P., The interval based control technique: Controlling physical systems through imprecise models, (Proc. Thirtieth IEEE Ind. Appl. Ann. Meeting, 2 (1995)), 1822-1827, Orlando, FL
[21] Wasfy, T.; Noor, A. K., Modeling and sensitivity analysis of multibody systems using new solid, shell and beam elements, Comput. Methods Appl. Mech. Engrg., 138, 187-211 (1996) · Zbl 0882.73050
[22] Wasfy, T., Modeling continuum multibody systems using the finite element method and element convected frames, Machine Elements and Machine Dynamics, (Proceedings of the 23rd ASME Mechanisms Conference. Proceedings of the 23rd ASME Mechanisms Conference, ASME DE, Vol. 71 (Sept. 1994)), 327-336, Minneapolis, MN
[23] Wasfy, T., A torsional spring-like beam element for the dynamic analysis of flexible multibody systems, Inter. J. Numer. Methods Engrg, 39, 7, 1079-1096 (1996) · Zbl 0879.73076
[24] Alexander, R. M.; Lawrence, K. L., Dynamic strains in a four-bar mechanism, (Proc. Third ASME Appl. Mech. Conf. (1973)), 268-274, Stillwater, OK
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.