Nonlinear Dynamics of Simple Shell Model with Chaotic Snapping Behavior
Publication: Journal of Engineering Mechanics
Volume 121, Issue 6
Abstract
A simple spring-mass numerical model (MSHELL), is developed as a tool to find appropriate integration time steps for nonlinear finite-element analysis. MSHELL possesses many features of nonlinearly deforming deep shells and, by matching some physical parameters of the MSHELL system and a nonlinear finite-element model (DSHELL), their dynamic behavior is both qualitatively and quantitatively similar. MSHELL is used to develop time-step criteria for both pre- and postsnapping behavior of a transversely point-loaded cylindrical shell. The criteria are then applied in a multiple-time-step method to DSHELL. The results indicate the simple model's correlation with the finite-element model and potential for saving computer time by changing the integration time step during a finite-element analysis based on MSHELL's behavior. Chaotic motion, characterized by one or more positive Lyapunov exponents, is seen in the simple model and likely explains unpredictable postcollapse results in the DSHELL finite-element code.
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References
1.
Adadan, A., and Huseyin, K.(1984). “An intrinsic method of harmonic analysis for non-linear oscillations: A perturbation technique.”J. Sound and Vibration, 95(4), 525–530.
2.
“ADINA theory and modeling guide.” (1987). Report ARD 87-8, ADINA R & D, Inc., Watertown, Mass.
3.
Budiansky, B. (1967). “Dynamic buckling of elastic structures: Criteria and estimates.”Dynamic stability of structures, G. Herrmann, ed., Pergamon, New York, N.Y., 83–106.
4.
Chien, L. S., and Palazotto, A. N.(1992a). “Dynamic buckling of composite cylindrical panels with high-order transverse shears subjected to a transverse concentrated load.”Int. J. Non-Linear Mech., 27(5), 719–734.
5.
Chien, L. S., and Palazotto, A. N.(1992b). “Nonlinear snapping considerations for laminated cylindrical panels.”Composites Engrg., 2(8), 631–639.
6.
Cook, R. D., Malkus, D. S., and Plesha, M. E. (1989). Concepts and applications of finite element analysis. John Wiley & Sons, New York, N.Y.
7.
El Naschie, M. S. (1990). Stress, stability and chaos in structural engineering: An energy approach . McGraw-Hill, Berkshire, England.
8.
Greer, J. M. Jr., and Palazotto, A. N.(1994). “Some nonlinear response characteristics of collapsing composite shells (TN).”AIAA J., 32(9), 1935–1938.
9.
Huseyin, K., and Yu, P.(1988). “On bifurcations into nonresonant quasi-periodic motions.”Appl. Math. Modelling, 12(2), 189–201.
10.
Katona, M. G., and Zienkiewicz, O. C. (1985). “A unified set of single step algorithms, part 3: The beta- m method, a generalization of the newmark scheme.”Int. J. Numer. Methods in Engrg., 21(7), 1345–1359.
11.
Kounadis, A.(1994). “A qualitative analysis for the local and global dynamic buckling and stability of autonomous discrete systems.”Q. J. Mech. and Appl. Math., 47(2), 269–295.
12.
Kounadis, A. N.(1991). “Chaoslike phenomena in the non-linear dynamic stability of discrete damped or undamped systems under step loading.”Int. J. Nonlinear Mech., 26(3/4), 103–311.
13.
Low, K. H.(1991). “On the accuracy of the numerical integral for the analysis of dynamic response.”Comput. & Struct., 44(3), 549–556.
14.
Maestrello, L., Frendi, A., and Brown, D. E.(1992). “Nonlinear vibration and radiation from a panel with transition to chaos.”AIAA J., 30(11), 2632–2638.
15.
Moon, F. C. (1987). Chaotic vibrations: An introduction for applied scientists and engineers . John Wiley & Sons, New York, N.Y.
16.
Nayfeh, A. H., and Mook, D. T. (1979). Nonlinear oscillations. John Wiley & Sons, New York, N.Y.
17.
Palazotto, A. N., and Dennis, S. T. (1992). Nonlinear anslysis of shell structures . Am. Inst. of Aeronautics and Astronautics, Washington, D.C.
18.
Palazotto, A. N., Chien, L. S., and Taylor, W. W.(1992). “Stability characteristics of laminated cylindrical panels under transverse loading.”AIAA J., 30(6), 1649–1653.
19.
Shaw, R. (1981). “Strange attractors, chaotic behavior, and information flow.”Z. Naturforsch, 36A, 80.
20.
Weaver, W. Jr., Timoshenko, S. P., and Young, D. H. (1990). Vibration problems in engineering . (5th ed.), John Wiley & Sons, New York, N.Y.
21.
Wolf, A., Swift, J. B., Swinney, H. L., and Vastano, J. A. (1985). “Determining lyapunov exponents from a time series.”Physica, 16D, 285–317.
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Copyright © 1995 American Society of Civil Engineers.
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Published online: Jun 1, 1995
Published in print: Jun 1995
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