Buckling, Vibration, and Flutter Behavior of Laminated Composite Panels with Flaws Subjected to Nonuniform Follower Forces
Publication: Journal of Engineering Mechanics
Volume 138, Issue 4
Abstract
The present work uses a finite-element approach to study vibration, buckling, and dynamic instability characteristics in damaged cross-ply and angle-ply curved panels. The panels are subjected to nonuniform, centrally, and edge-distributed follower loading. First order shear-deformation theory was used to model the doubly curved panels and was formulated in accordance with Sanders’ first approximation. An anisotropic damage formulation was used to model damage. An analysis was carried out on plate and shallow shells to obtain vibration, buckling, and static instability (i.e., divergence) and dynamic instability (i.e., flutter) behavior. The effects of load type, load width, damage, and damage location on natural frequency, buckling load, divergence load, flutter load and flutter frequency were studied. The effect of curvature to improve the stability characteristics of panels is discussed. The desirable position of damage on a panel is discussed on the basis of different stability behavior. Results indicate that narrow edge loading is undesirable in most cases.
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References
Adali, S. (1982). “Stability of a rectangular plate under nonconservative and conservative forces.” Int. J. Solids Struct., 18(12), 1043–1052.
Beck, M. (1952). “Die Knicklast des einseitig eingespannten, tangential gedrückten Stabes.” Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 3(3), 225–228.
Bolotin, V. (1963). Nonconservative problems of the theory of elastic stability, 1st Ed., MacMillan, London.
Culkowski, P., and Reismann, H. (1977). “Plate buckling due to follower edge forces.” J. Appl. Mech., 44(4), 768–769.
Datta, P., and Deolasi, P. (1996). “Dynamic instability characteristics of plates subjected to partially distributed follower edge loading with damping.” Proc., Institution of Mechanical Engineers. Part C. Journal of Mechanical Engineering Science, 210(5), 445–452.
Elishakoff, I. (2005). “Controversy associated with the so-called ‘follower forces’: Critical overview.” Appl. Mech. Rev., 58(2), 117–142.
Gendy, A., Saleeb, A., and Mikhail, S. (1997). “Free vibrations and stability analysis of laminated composite plates and shells with hybrid/mixed formulation.” Comput. Struct., 63(6), 1149–1163.
Huang, N. (1994). “Influence of shear correction factors in the higher order shear deformation laminated shell theory.” Int. J. Solids Struct., 31(9), 1263–1277.
Khdeir, A., and Reddy, J. (1999). “Free vibrations of laminated composite plates using second-order shear deformation theory.” Comput. Struct, 71(6), 617–626.
Kim, J., and Kim, H. (2000). “A study on the dynamic stability of plates under a follower force.” Comput. Struct., 74(3), 351–363.
Kumar, L. R., Datta, P., and Prabhakara, D. (2003). “Dynamic instability characteristics of laminated composite plates subjected to partial follower edge load with damping.” Int. J. Mech. Sci., 45(9), 1429–1448.
Moorthy, J., Reddy, J., and Plaut, R. (1990). “Parametric instability of laminated composite plates with transverse shear deformation.” Int. J. Solids Struct., 26(7), 801–811.
Nair, L. S., Singh, G., and Rao, G. V. (1996). “Stability of laminated composite plates subjected to various types of in-plane loadings.” Int. J. Mech. Sci., 38(2), 191–202.
Narita, Y., and Leissa, A. (1990). “Buckling studies for simply supported symmetrically laminated rectangular plates.” Int. J. Mech. Sci., 32(11), 909–924.
Nikolai, E. (1928). “On the stability of the rectilinear form of equilibrium of a bar in compression and torsion.” Izvest. Leningrad Politekhn in-ta, 31, 357–387 (in Russian).
Pflüger, A. (1955). “Zur Stabilitat des tangential gedruckten Stabes.” Zeitschrift fur Angewandte Mathematik und Mechanik (ZAMM), 35(5), 191.
Prabhakara, D., and Datta, P. (1993a). “Parametric instability characteristics of rectangular plates with localized damage subjected to in-plane periodic load.” Struct. Eng. Rev., 5(1), 71–79.
Prabhakara, D., and Datta, P. (1993b). “Vibration and static stability characteristics of rectangular plates with a localized flaw.” Comput. Struct,, 49(5), 825–836.
Putcha, N., and Reddy, J. (1986). “Stability and natural vibration analysis of laminated plates by using a mixed element based on a refined plate theory.” J. Sound Vib., 104(2), 285–300.
Reddy, J. (1984). An introduction to the finite element method, 2nd Ed., McGraw-Hill, New York.
Reddy, J., and Phan, N. (1985). “Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory.” J. Sound Vib., 98(2), 157–170.
Reut, V. (1939). “About the theory of elastic stability.” Proc., Odessa Institute of Civil and Communal Engineering, 126–138.
Sugiyama, Y. (1982). “Buckling of generalized Reut rod.” SM Arch., 7, 433–466.
Sugiyama, Y., Langthjem, M., and Ryu, B. (1999). “Realistic follower forces.” J. Sound Vib., 225(4), 779–782.
Udar, R., and Datta, P. (2008). “Combination resonance instability of curved panels with cutout subjected to nonuniform loading with damping.” J. Eng. Mech., 134(7), 555–566.
Valliappan, S., Murti, V., and Wohua, Z. (1990). “Finite element analysis of anisotropic damage mechanics problems.” Eng. Fract. Mech., 35(6), 1061–1071.
Yu, W., Hodges, D., and Volovoi, V. (2002). “Asymptotic construction of Reissner-like composite plate theory with accurate strain recovery.” Int. J. Solids Struct., 39(20), 5185–5203.
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Information
Published In
Journal of Engineering Mechanics
Volume 138 • Issue 4 • April 2012
Pages: 347 - 357
Copyright
© 2012 American Society of Civil Engineers.
History
Received: Feb 19, 2010
Accepted: Sep 2, 2011
Published online: Sep 5, 2011
Published in print: Apr 1, 2012
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