Research Papers

A Partition Expansion Method for Nonlinear Response Analysis of Stochastic Dynamic Systems With Local Nonlinearity

[+] Author and Article Information
Changqing Bai

State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an 710049, China e-mail: baichq@mail.xjtu.edu.cn

Hongyan Zhang

School of Science, Chang'an University, Xi'an 710064, China

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Design Engineering Division. Manuscript received July 21, 2011; final manuscript received November 26, 2012; published online January 7, 2013. Assoc. Editor: Henryk Flashner.

J. Comput. Nonlinear Dynam 8(3), 031009 (Jan 07, 2013) (7 pages) Paper No: CND-11-1114; doi: 10.1115/1.4023163 History: Received July 21, 2011; Revised November 26, 2012

This paper focuses on the problem of nonlinear dynamic response variability resulting from stochastic system properties and random loads. An efficient and accurate method, which can be employed to analyze the dynamic responses of random finite element systems with local nonlinearity, is presented in this paper. This method, dubbed as the partition expansion method, is based on the partitioned time integration algorithm in conjunction with the Neumann expansion technique within the framework of the Monte Carlo simulation. Two numerical examples involving structural and mechanical stochastic vibration problems are employed to illustrate the advantage of the proposed method with respect to accuracy and efficiency. By comparing the results obtained by the direct Monte Carlo simulation, the dynamic response statistics can be accurately determined using the proposed method with four order expansion while the computational efforts are significantly reduced. The comparison of computing time indicates that the proposed method is efficient and practical for analyzing the statistical quantities of stochastic dynamic systems with local nonlinearity.

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Ibrahim, R. A., 1987, “Structural Dynamics With Parameter Uncertainties,” Appl. Mech. Rev., 40(3), pp. 309–328. [CrossRef]
Benaroya, H., and Rehak, M., 1988, “Finite Element Methods in Probabilistic Structural Analysis: A Selective Review,” Appl. Mech. Rev., 41(5), pp. 201–213. [CrossRef]
Chang, C. C., and Yang, H. T. Y., 1991, “Random Vibration of Flexible, Uncertain Beam Element,” ASCE J. Eng. Mech., 117(10), pp. 2329–2350. [CrossRef]
Zhang, S. W., Ellingwood, B., Corotis, R., and Zhang, J., 1995, “Direct Integration Method for Stochastic Finite-Element Analysis of Nonlinear Dynamic Response,” Struct. Eng. Mech., 3(3), pp. 273–287.
Brenner, C. E., and Bucher, C., 1995, “A Contribution to the SFE-Based Reliability Assessment of Nonlinear Structures Under Dynamic Loading,” Prob. Eng. Mech., 10(4), pp. 265–273. [CrossRef]
Schueller, G. I., and Pradlwarter, H. J., 1999, “On the Stochastic Response of Nonlinear FE Models,” Arch. Appl. Mech., 69(9–10), pp. 765–784. [CrossRef]
Huh, J., and Haldar, A., 2001, “Stochastic Finite-Element-Based Seismic Risk of Nonlinear Structures,” ASCE J. Struct. Eng., 127(3), pp. 323–329. [CrossRef]
Moon, B. Y., Kang, G. J., Kang, B. S., and Cho, D. S., 2004, “Dynamic and Reliability Analysis of Stochastic Structure System Using Probabilistic Finite Element Method,” Struct. Eng. Mech., 18(1), pp. 125–135.
Falsone, G., and Ferro, G., 2006, “A Dynamical Stochastic Finite Element Method Based on the Moment Equation Approach for the Analysis of Linear and Nonlinear Uncertain Structures,” Struct. Eng. Mech., 23(6), pp. 599–613.
Li, J., and Chen, J. B., 2007, “The Number Theoretical Method in Response Analysis of Nonlinear Stochastic Structures,” Comput. Mech., 39(6), pp. 693–708. [CrossRef]
Haciefendioglu, K., Basaga, H. B., Bayraktar, A., and Ates, S., 2007, “Nonlinear Analysis of Rock-Fill Dams to Non-Stationary Excitation by the Stochastic Wilson-Theta Method,” Appl. Math. Comput., 194(2), pp. 333–345. [CrossRef]
Chang, T. P., Liu, M. F., and Chang, H. C., 2008, “Finite Element Analysis of Nonlinear Shell Structures With Uncertain Material Property,” Thin-Walled Struct., 46(10), pp. 1055–1065. [CrossRef]
Lal, A., and Singh, B., 2009, “Stochastic Nonlinear Free Vibration of Laminated Composite Plates Resting on Elastic Foundation in Thermal Environments,” Comput. Mech., 44(1), pp. 15–29. [CrossRef]
Chen, J. B., and Li, J., 2010, “Stochastic Seismic Response Analysis of Structures Exhibiting High Nonlinearity,” Comput. Struct., 88(7–8), pp. 395–412. [CrossRef]
Xu, J. X., and Zheng, T. S., 1993, Numerical Methods for Dynamic Analysis of Structures, Xi'an Jiaotong University Press, Beijing.
Yamazaki, F., Shinozuka, M., and Dasgupta, G., 1988, “Neumann Expansion for Stochastic Finite Element Analysis,” ASCE J. Eng. Mech., 114, pp. 1335–1354. [CrossRef]
Zienkiewicz, O. C., 1977, The Finite Element Method, McGraw-Hill Company, London.
Guo, Y. B., Shim, V. P. W., and Yeo, A. Y. L., 2010, “Elastic Wave And Energy Propagation in Angled Beams,” Acta Mech., 214, pp. 79–94. [CrossRef]
Chan, S. L., and Chui, P. P. T., 2000, Nonlinear Static and Cyclic Analysis of Steel Frames With Semi-Rigid Connections, Elsevier, Amsterdam.
Bai, C. Q., Xu, Q. Y., and Wang, J. Y., 2011, “Effects of Flexible Support Stiffness on the Nonlinear Dynamic Characteristics and Stability of a Turbopump Rotor System,” Nonlinear Dyn., 64, pp. 237–252. [CrossRef]


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Fig. 1

Angled beam subjected to impact loads

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Fig. 2

Mean value of nonlinear angular displacement of angled beam

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Fig. 3

Standard deviation of nonlinear angular displacement of angled beam

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Fig. 4

Standard deviation error of angular displacement as a function of sample size

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Fig. 5

Turbopump rotor-seal system

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Fig. 6

Mean value of nonlinear displacement response of rotor-seal system

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Fig. 7

Standard deviation of nonlinear displacement response of rotor-seal system

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Fig. 8

Standard deviation error of displacement response as a function of sample size



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