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.

References

References
1.
Ibrahim
,
R. A.
,
1987
, “
Structural Dynamics With Parameter Uncertainties
,”
Appl. Mech. Rev.
,
40
(
3
), pp.
309
328
.10.1115/1.3149532
2.
Benaroya
,
H.
, and
Rehak
,
M.
,
1988
, “
Finite Element Methods in Probabilistic Structural Analysis: A Selective Review
,”
Appl. Mech. Rev.
,
41
(
5
), pp.
201
213
.10.1115/1.3151892
3.
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
.10.1061/(ASCE)0733-9399(1991)117:10(2329)
4.
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
.
5.
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
.10.1016/0266-8920(95)00021-6
6.
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
.10.1007/s004190050255
7.
Huh
,
J.
, and
Haldar
,
A.
,
2001
, “
Stochastic Finite-Element-Based Seismic Risk of Nonlinear Structures
,”
ASCE J. Struct. Eng.
,
127
(
3
), pp.
323
329
.10.1061/(ASCE)0733-9445(2001)127:3(323)
8.
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
.
9.
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
.
10.
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
.10.1007/s00466-006-0054-9
11.
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
.10.1016/j.amc.2007.04.053
12.
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
.10.1016/j.tws.2008.01.017
13.
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
.10.1007/s00466-008-0352-5
14.
Chen
,
J. B.
, and
Li
,
J.
,
2010
, “
Stochastic Seismic Response Analysis of Structures Exhibiting High Nonlinearity
,”
Comput. Struct.
,
88
(
7–8
), pp.
395
412
.10.1016/j.compstruc.2009.12.002
15.
Xu
,
J. X.
, and
Zheng
,
T. S.
,
1993
,
Numerical Methods for Dynamic Analysis of Structures
,
Xi'an Jiaotong University Press
,
Beijing
.
16.
Yamazaki
,
F.
,
Shinozuka
,
M.
, and
Dasgupta
,
G.
,
1988
, “
Neumann Expansion for Stochastic Finite Element Analysis
,”
ASCE J. Eng. Mech.
,
114
, pp.
1335
1354
.10.1061/(ASCE)0733-9399(1988)114:8(1335)
17.
Zienkiewicz
,
O. C.
,
1977
,
The Finite Element Method
,
McGraw-Hill Company
,
London
.
18.
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
.10.1007/s00707-010-0317-6
19.
Chan
,
S. L.
, and
Chui
,
P. P. T.
,
2000
,
Nonlinear Static and Cyclic Analysis of Steel Frames With Semi-Rigid Connections
,
Elsevier
,
Amsterdam
.
20.
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
.10.1007/s11071-010-9858-4
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