The nonlinear response of shallow shells subjected to combined acoustic and thermal loads is analyzed using an efficient nonlinear modal finite element (FE) formulation. The acoustic loads have non-Gaussian probabilistic characteristics and are simulated by an algorithm capable of reliably converging to a target power spectral density (PSD) function and marginal probability density function (PDF). Factors contributing to the panel structural stiffness, softening and hardening effects, and modal contribution are also investigated along with their impact on the root-mean-square responses. The Palmgren–Miner cumulative damage theory in combination with the rainflow counting (RFC) cycles methods was used to estimate the panel fatigue life. Parametric studies for cylindrical and spherical curved panels considering stacking laminations, radii of curvatures, acoustic and thermal loads are studied in detail.

References

1.
Holehouse
,
I.
,
1980
, “
Sonic Fatigue Design Techniques for Advanced Composites Aircraft Structures
,” Wright-Patterson AFB, OH, Technical Report No. AFWL-TR-80-3019.
2.
Rudder
,
F. F.
, and
Plumbee
,
H. E.
,
1975
, “
Sonic Fatigue Design Guide for Military Aircraft
,” Wright-Patterson AFB, OH, Technical Report No. AFFDL-TR-74-112.
3.
Steinwolf
,
A.
, and
Rizzi
,
S. A.
,
2003
, “
Reverse Non-Gaussian PDF Modeling of Turbulent Boundary Layer Fluctuation Pressure Excitation
,”
VIII International Conference on recent Advances in Structural Dynamics
, Southampton, UK, July 14–16, Paper No. 8.
4.
Shinozuka
,
M.
, and
Deodatis
,
G.
,
1991
, “
Simulation of Stochastic Processes by Spectral Representation
,”
ASME Appl. Mech. Rev.
,
44
(
4
), pp.
191
204
.10.1115/1.3119501
5.
Shinozuka
,
M.
, and
Deodatis
,
G.
,
1996
, “
Simulation of Multi-Dimensional Gaussian Stochastic Fields by Spectral Representation
,”
ASME Appl. Mech. Rev.
,
49
(
1
), pp.
29
53
.10.1115/1.3101883
6.
Shinozuka
,
M.
, and
Jan
,
C. M.
,
1972
, “
Digital Simulation of Random Processes and Its Applications
,”
J. Sound Vib.
,
25
(
1
), pp.
111
128
.10.1016/0022-460X(72)90600-1
7.
Grigoriu
,
M.
,
1984
, “
Crossing of Non-Gaussian Translation Processes
,”
ASCE J. Eng. Mech.
,
110
(
EM4
), pp.
610
620
.10.1061/(ASCE)0733-9399(1984)110:4(610)
8.
Deodatis
,
G.
, and
Micaletti
,
R.
,
2001
, “
Simulation of Highly Skewed Non-Guassian Stochastic Processes
,”
ASCE J. Eng. Mech.
,
127
(
12
), pp.
1284
1295
.10.1061/(ASCE)0733-9399(2001)127:12(1284)
9.
Shinozuka
,
M.
,
1987
, “
Stochastic Fields and Their Digital Simulation
,”
Stochastic Methods in Structural Dynamics
,
G. I.
Schueller
, and
M.
Shinozuka
, eds.,
Matinus Hijhoff Publishers
,
Dordrecht, Germany
, pp.
93
133
.
10.
Borgman
,
L. E.
,
1990
,
Irregular Ocean Waves: Kinematics and Forces
,”
Prentice Hall
,
Upper Saddle River, NJ
.
11.
Grigoriu
,
M.
,
1993
, “
On the Spectral Representation Method in Simulation
,”
Probab. Eng. Mech.
,
8
(
2
), pp.
17
90
.
12.
Kameda
,
H.
, and
Morikawa
,
H.
,
1993
, “
Conditioned Stochastic Processes for Conditional Random Fields
,”
ASCE J. Eng. Mech.
,
120
(
4
), pp.
855
875
.10.1061/(ASCE)0733-9399(1994)120:4(855)
13.
Cai
,
G. Q.
, and
Lin
,
Y.
,
1996
, “
Generation of Non-Gaussian Stationary Stochastic Processes
,”
Phys. Rev.
,
54
(
1
), pp.
299
303
.
14.
Gurley
,
K.
, and
Kareem
,
A.
,
1997
, “
Analysis, Interpretation, Modeling and Simulation of Unsteady Wind and Pressure Data
,”
J. Wind Eng. Ind. Aerodyn.
,
543
(69), pp.
657
669
.10.1016/S0167-6105(97)00195-5
15.
Grigoriu
,
M.
, “
Simulation of Stationary Non-Gaussian Translation Processes
,”
ASCE J. Eng. Mech.
,
124
(
2
), pp.
121
126
.10.1061/(ASCE)0733-9399(1998)124:2(121)
16.
Popescu
,
R.
,
Deodatis
,
G.
, and
Prevost
,
J. H.
,
1998
, “
Simulation of Homogeneous, Non-Gaussian, Stochastic Vector Fields
,”
Probab. Eng. Mech.
,
13
(
1
), pp.
1
13
.10.1016/S0266-8920(97)00001-5
17.
Poirion
,
F.
, and
Soize
,
C.
,
1999
, “
Monte Carlo Construction of Karhunen Loeve Expansion for Non-Gaussian Random Fields
,”
Proceedings of the 13th ASCE Engineering Mechanics Conference
, Baltimore, MD, June 13–16.
18.
Yamazaki
,
F.
, and
Shinozuka
,
M.
,
1988
, “
Digital Generation of Non-Gaussian Stochastic Fields
,”
ASCE J. Eng. Mech.
,
114
(
7
), pp.
1183
1197
.10.1061/(ASCE)0733-9399(1988)114:7(1183)
19.
Masters
,
F.
, and
Gurley
,
K.
,
2003
, “
Non-Gaussian Process Simulation: CDF Map-Based Spectral Correction
,”
ASCE J. Eng. Mech.
,
129
(
12
), pp.
1418
1428
.10.1061/(ASCE)0733-9399(2003)129:12(1418)
20.
Vaicaitis
,
R.
, and
Kavallieratos
,
P. A.
,
1993
, “
Nonlinear Response of Composite Panels to Random Excitation
,”
Proceedings of 34th Structures, Structural Dynamics, and Materials Conference
, La Jolla, CA, April 19–23, pp.
1041
1049
.
21.
Arnold
,
R. R.
, and
Vaicaitis
,
R.
,
1992
, “
Nonlinear Response and Fatigue of Surface Panels by the Time Domain Monte Carlo Approach
,” Wright-Patterson AFB, OH, Technical Report No. WRDC-TR-90-3081.
22.
Lee
,
J.
,
1995
, “
Improving the Equivalent Linearization Technique for Stochastic Duffing Oscillators
,”
J. Sound Vib.
,
186
(
5
), pp.
846
855
.10.1006/jsvi.1995.0492
23.
Roberts
,
J. B.
, and
Spanos
,
P. D.
,
1990
,
Random Vibration of Statistical Linearization
,
Wiley
,
New York
.
24.
Robinson
,
J. H.
,
1990
, “
Finite Element Formulation and Numerical Simulation of the Large Deflection Random Vibration of Laminated Composite Plates
,” M.S. thesis, Old Dominion University, Norfolk, VA.
25.
Green
,
P. D.
, and
Killey
,
A.
,
1997
, “
Time Domain Dynamic Finite Element Modeling in Acoustic Fatigue Design
,”
Proceedings of 6th International Conference on Structural Dynamics
, ISVR, University of Southampton, UK, July 7, pp.
1007
1026
.
26.
Locke
,
J. E.
,
1988
, “
A Finite Element Formulation for the Large Deflection Random Response of Thermally Buckled Structures
,” Ph.D. dissertation, Old Dominion University, Norfolk, VA.
27.
Xue
,
D.
, and
Mei
,
C.
,
1993
, “
Finite Element Nonlinear Panel Flutter With Arbitrary Temperatures in Supersonic Flow
,”
AIAA J.
,
31
(
1
), pp.
154
162
.10.2514/3.11332
28.
Mei
,
C.
,
Dhainaut
,
J. M.
,
Duan
,
B.
,
Spotswwood
,
S. M.
, and
Wolfe
,
H. F.
,
2000
, “
Nonlinear Random Response of Composite Panels in an Elevated Thermal Environment
,” WPAFB, OH, Technical Report No. AFRL-VA-WP-TR-2000-3049.
29.
Dhainaut
,
J. M.
,
2001
, “
Nonlinear Response and Fatigue Estimation of Surface Panels to White and Non-White Gaussian Random Excitations
,” Ph.D. dissertation, Old Dominion University, Norfolk, VA.
30.
Mei
,
C.
, and
Wolfe
,
H. F.
,
1986
, “
On Large Deflection Analysis in Acoustic Fatigue Design
,”
Random Vibration: Status and Recent Development, The S.H. Crandall Festschrift
,
Elsevier Science
,
Amsterdam, The Netherlands
, pp.
279
302
.
31.
Benaroya
,
H.
, and
Rebak
,
M.
,
1988
, “
Finite Element Methods in Probabilistic Structural Analysis: A Selective Review
,”
ASME Appl. Mech. Rev.
,
41
(
5
), pp.
201
213
.10.1115/1.3151892
32.
Clarkson
,
B. L.
,
1994
, “
Review of Sonic Fatigue Technology
,” NASA Report No. NASA CR-4587.
33.
Vaicaitis
,
R.
,
1994
, “
Nonlinear Response and Sonic Fatigue of National Aerospace Plane Surface Panels
,”
J. Aircr.
,
31
(
1
), pp.
10
18
.10.2514/3.46449
34.
Dhainaut
,
J. M.
,
Cheng
,
G.
, and
Mei
,
C.
,
2007
, “
Response of Plates Under Statistically Unsynchronized Uniform Random Loads Using Monte-Carlo Simulation
,”
J. Comput. Appl. Mech.
,
8
(
1
), pp. 3–18.
35.
Dhainaut
,
J.-M.
,
Guo
,
X.
, and
Mei
,
C.
,
2008
, “
Nonlinear Response of Thin Shells Subjected to Unsynchronized Random Loads in Time
,” Paper No.
AIAA
2008-1875.102514/6.2008-1875
36.
Przekop
,
A.
,
Guo
,
X.
,
Azzous
,
S.
, and
Mei
,
C.
,
2003
, “
Nonlinear Response and Fatigue Life of Shallow Shells to Acoustic Excitation Using Finite Element
,” 44th
AIAA/ASME/ASCE/AHS/ASC
Structures, Structural Dynamics, and Materials Conference
, Apr. 7−10, Norfolk, VA, Paper No. AIAA-2003-1710.10.2514/6.2003-1710
37.
Benasciutti
,
D.
, and
Tove
,
R.
,
2007
, “
On Fatigue Damage Assessment in Bimodal Processes
,”
Int. J. Fatigue
,
29
(
2
), pp.
232
244
.10.1016/j.ijfatigue.2006.03.013
38.
Miner
,
M. A.
,
1945
, “
Cumulative Damage in Fatigue
,”
ASME J. Appl. Mech.
,
12
(3), pp.
A159
A164
.
39.
Palmgren
,
A.
,
1924
, “
Die Lebensdauer von Kugellagern
,”
Zeitshrift des Vereines Deutsher Ingenieure
,
68
(
14
), pp.
339
341
.
40.
Dowling
,
N. E.
,
1972
, “
Fatigue Failure Predictions for Complicated Stress–Strain Histories
,”
J. Mater.
,
7
(
1
), pp.
71
87
.
41.
Matsuishi
,
M.
, and
Endo
,
T.
,
1968
, “
Fatigue of Metals Subject to Varying Stress
,” Japan Society of Mechanical Engineers, Fukuoka, Japan, Mar., pp.
37
40
.
42.
Rychlik
,
I.
,
1988
, “
Rain-Flow Cycle Distribution for Ergodic Load Processes
,”
SIAM J. Appl. Math.
,
48
(
3
), pp.
662
679
.10.1137/0148037
43.
Dirlik
,
T.
,
1985
, “
Application of Computers in Fatigue Analysis
,” Ph.D. dissertation, University of Warwick, Coventry, UK.
44.
Bishop
,
N. W. N.
, and
Sherratt
,
F.
,
1989
, “
Fatigue Life Prediction from Power Spectral Density Data. Part 1. Traditional Approaches and Part 2
,”
Recent Developments in Environmental Engineering
,
Trade Publication
, Vol.
2
, Nos. 1 and 2.
45.
Bishop
,
N. W. N.
, and
Sherratt
,
F.
,
1990
, “
A Theoretical Solution for the Estimation of Rain-Flow Ranges From Power Spectral Density Data
,”
Fatigue Fract. Eng. Mater. Struct.
,
13
(
4
), pp.
311
326
.10.1111/j.1460-2695.1990.tb00604.x
46.
Gurley
,
K.
, and
Kareem
,
A.
,
1998
, “
A Multi-Variate Non-Gaussian Simulation Algorithm
,”
4th International Conference on Stochastic Structural Dynamics
, Notre Dame, IN, Aug. 6–8.
47.
Gurley
,
K.
, and
Kareem
,
A.
,
1998
, “
A Conditional Simulation of Non-Normal Velocity/Pressure Fields
,”
J. Wind Eng. Ind. Aerodyn.
,
77–78
, pp.
39
51
.10.1016/S0167-6105(98)00130-5
48.
Brodtkorb
,
P. A.
,
Johannesson
,
P.
,
Lindgren
,
G.
,
Rychlik
,
I.
,
Ryden
,
J.
, and
Sjo
,
E.
,
2000
, “
WAFO-A Matlab Toolbox for Analysis of Random Waves and Loads
,”
Proceedings of the 10th International Offshore and Polar Engineering Conference
, Seattle, WA, Vol. III, pp.
343
350
.
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