Reduction method for finite element nonlinear dynamic analysis of shells

AIAA Journal

Volumn 49, Issue 10, 2011, Pages 2295-2304

  Tiso, Paolo ^a   Jansen, Eelco ^b   Abdalla, Mostafa ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DISPLACEMENT FIELD; FINITE ELEMENT; GEOMETRICAL NON-LINEARITY; LINEAR PROBLEMS; MODAL BASIS; NON-LINEAR DYNAMIC ANALYSIS; NON-LINEAR DYNAMICS; NONLINEAR BEHAVIOR; NUMBER OF DEGREES OF FREEDOM; REDUCTION METHOD; SECOND ORDER MODES; STATIC EQUILIBRIUM CONFIGURATIONS; VIBRATION MODES;

DYNAMIC ANALYSIS; DYNAMIC LOADS; EQUATIONS OF MOTION; NONLINEAR EQUATIONS; PERTURBATION TECHNIQUES; VIBRATING CONVEYORS;

FINITE ELEMENT METHOD;

EID: 80053507707     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/1.J051003     Document Type: Article

References (33)

1. Kunisch, K., and Volkwein, S., "Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics," SIAM Journal on Numerical Analysis, Vol. 40, No. 2, 2002, pp. 492-515. doi:10.1137/S0036142900382612
2. Shao, A., Xi, S., and Qiu, C., "A Variational Method for Correcting Nonsystematic Errors In Numerical Weather Prediction," Science in China Series B, Chemistry, Life Sciences and Earth Sciences, Vol. 52, 2009, pp. 1650-1660. doi:10.1007/s11430-009-0139-3
3. Price, N. D., Reed, J. L., Papin, J. A., Famili, I., and Palsson, B. O., "Analysis of Metabolic Capabilities Using Singular Value Decomposition of Extreme Pathway Matrices," Biophysical Journal, Vol. 84, No. 2, 2003, pp. 794-804. doi:10.1016/S0006-3495(03)74899-1 (Pubitemid 36133408)
4. Krysl, P., Lall, S., and Marsden, J. E., "Dimensional Model Reduction in Non-Linear Finite Element Dynamics of Solids and Structures," International Journal for Numerical Methods in Engineering, Vol. 51, 2001, pp. 479-504. doi:10.1002/nme.167 (Pubitemid 32411907)
5. Meyer, M., and Matthies, H. G., "Efficient Model Reduction In Nonlinear Dynamics Using the Karhunen-Love Expansion and Dual- Weighted-Residual Methods," Computational Mechanics, Vol. 31, No. 1, 2003, pp. 179-191. doi:10.1007/s00466-002-0404-1
6. Zilian, A., Dinkler, D., and Vehre, A., "Projection-Based Reduction of Fluid-Structure Interaction Systems Using Monolithic Space-Time Modes," Computer Methods in Applied Mechanics and Engineering, Vol. 198, No. 47-48, 2009, pp. 3795-3805. doi:10.1016/j.cma.2009.08.010
7. Rizzi, S. A., and Przekop, A., "System Identification-Guided Basis Selection for Reduced-Order Nonlinear Response Analysis," Journal of Sound and Vibration, Vol. 315, No. 3, 2008, pp. 467-485. doi:10.1016/j.jsv.2007.12.031
8. Weickum, G., Eldred, M., and Maute, K., "AMultipoint Reduced-Order Modeling Approach of Transient Structural Dynamics with Application to Robust Design Optimization," Structural and Multidisciplinary Optimization, Vol. 38, 2009, pp. 599-611. doi:10.1007/s00158-008-0309-5
9. Bruls, O., and Eberhard, P., "Sensitivity Analysis for Dynamic Mechanical Systems with Finite Rotations," International Journal for Numerical Methods in Engineering, Vol. 74, 2008, pp. 1897-1927. doi:10.1002/nme.2232
10. Jacob, B. P., and Ebecken, N. F. F., "Adaptive Reduced Integration Method for Nonlinear Structural Dynamic Analysis," Computers and Structures, Vol. 45, No. 2, 1992, pp. 333-347. doi:10.1016/0045-7949(92)90417-X (Pubitemid 23570411)
11. Hollkamp, J. J., Gordon, R. W., and Spottswood, S. M., "Nonlinear Modal Models for Sonic Fatigue Response Prediction: A Comparison Of Methods," Journal of Sound and Vibration,Vol. 284, No. 3-5, 2005, pp. 1145-1163. doi:10.1016/j.jsv.2004.08.036 (Pubitemid 40643854)
12. Spottswood, S., Hollkamp, J., and Eason, T., "Reduced-Order Models for a Shallow Curved Beam Under Combined Loading," AIAA Journal, Vol. 48, No. 1, 2010, pp. 47-55. doi:10.2514/1.38707
13. Mignolet, M., Radu, A., and Gao, X., "Validation of Reduced Order Modeling for the Prediction of the Response and Fatigue Life of Panels Subjected to Thermo-Acoustic Effects," Proceedings of the 8th International Conference on Recent Advances in Structural Dynamics, Southampton, England, U.K., 2003.
14. Spottswood, S., Eason, T., Wang, X., and Mignolet, M., "Nonlinear Reduced Order Modelling of Curved Beams: A Comparison of Methods," Proceedings of the 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Palm Springs, CA, 2009.
15. Przekop, A., and Rizzi, S. A., "A Reduced Order Method for Predicting High Cycle Fatigue of Nonlinear Structures," Computers and Structures, Vol. 84, Nos. 24-25, 2006, pp. 1606-1618. doi:10.1016/j.compstruc. 2006.01.015 (Pubitemid 44189487)
16. Rewienski, M., and White, J., "Model Order Reduction for Nonlinear Dynamical Systems Based on Trajectory Piecewise-Linear Approximations," Linear Algebra and Its Applications, Vol. 415, 2006, pp. 426-454. doi:10.1016/j.laa.2003.11.034
17. Idelsohn, S. R., and Cardona, A., "A Reduction Method for Nonlinear Structural Dynamic Analysis," Computer Methods in Applied Mechanics and Engineering, Vol. 49, 1985, pp. 253-279. doi:10.1016/0045-7825(85)90125-2 (Pubitemid 15530399)
18. Idelsohn, S. R., and Cardona, A., "A Load-Dependent Basis for Reduced Nonlinear Structural Dynamics," Computers and Structures, Vol. 20, 1985, pp. 203-210. doi:10.1016/0045-7949(85)90069-0
19. Slaats, P. M. A., de Jong, J., and Sauren, A. A. H. J., "Model Reduction Tools for Nonlinear Structural Dynamics," Computers and Structures, Vol. 54, 1995, pp. 1155-1171. doi:10.1016/0045-7949(94)00389-K
20. Barbič, J., and James, D. L., "Real-Time Subspace Integration for St. Venant-Kirchhoff Deformable Models," ACM Transactions on Graphics, Vol. 24, No. 3, 2005, pp. 982-990. doi:10.1145/1073204.1073300
21. Budiansky, B., "Dynamic Buckling of Elastic Structures: Criteria and Estimates," Dynamic Stability of Structures, Proceedings of International Conference in Organic Coatings Science and Technology, Pergamon, New York, 1965.
22. Byskov, E., and Hutchinson, J. W., "Mode Interaction in Axially Stiffened Cylindrical Shells," AIAA Journal, Vol. 15, 1977, pp. 941-948. doi:10.2514/3.7388
23. Tiso, P., Abdalla, M., and Jansen, E., "Koiter's Postbuckling Analysis of General Shell Structures Using the Finite Element Method," Proceedings of the 25th International Congress of the Aeronautical Sciences, Hamburg, Germany, 2006.
24. Rahman, T., and Jansen, E., "Finite Element Based Coupled Mode Initial Postbuckling Analysis of a Composite Cylindrical Shell," Thin- Walled Structures, Vol. 48, 2010, pp. 25-32. doi:10.1016/j.tws.2009.08.003
25. Chen, H., and Virgin, L., "Finite Element Analysis Of Postbuckling Dynamics in Plates. Part I: An Asymptotic Approach," International Journal of Solids and Structures, Vol. 43, 2006, pp. 3983-4007. doi:10.1016/j.ijsolstr. 2005.04.036
26. Tiso, P., and Jansen, E., "A Finite Element Based Reduction Method for Nonlinear Analysis of Structures," Proceedings of the 46th AIAA/ ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2005.
27. Wedel-Heinen, J., "Vibration of Geometrically Imperfect Beam and Shell Structures," International Journal of Solids and Structures, Vol. 27, 1991, pp. 29-47. doi:10.1016/0020-7683(91)90143-4
28. Rehfield, L. W., "Nonlinear Vibration of Elastic Structures," International Journal of Solids and Structures, Vol. 9, 1973, pp. 581- 590. doi:10.1016/0020-7683(73)90071-1
29. Jansen, E., "A Perturbation Method for Nonlinear Vibrations of Imperfect Structures: Application to Cylindrical Shell Vibrations," International Journal of Solids and Structures, Vol. 45, Feb. 2008, pp. 1124-1145. doi:10.1016/j.ijsolstr.2007.07.007 (Pubitemid 350088766)
30. Tiso, P., and Jansen, E., "A Finite Element Based Perturbation Method for Nonlinear Free Vibration of Structures," Proceedings of the 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Honolulu, 2007.
31. Felippa, C., and Militello, C., "Construction of Optimal 3-Node Plate Bending Triangles by Templates," Computational Mechanics, Vol. 24, 1999, pp. 1-13. doi:10.1007/s004660050433
32. Bergan, P., and Felippa, C., "A Triangular Membrane Element with Rotational Degrees of Freedom," Computer Methods in Applied Mechanics and Engineering, Vol. 50, 1985, pp. 25-69. doi:10.1016/0045-7825(85)90113-6 (Pubitemid 15588703)
33. Bathe, K. J., Finite Element Procedures, Prentice-Hall, Upper Saddle River, NJ, 1996.