Lock-free material finite element for non-linear oscillations of laminated plates

Journal of Sound and Vibration

Volumn 230, Issue 2, 2000, Pages 221-240

  Singh, Gajbir ^a   Venkateswara Rao, G ^a  

^a INDIAN SPACE RESEARCH ORGANISATION   (India)

Author keywords

[No Author keywords available]

Indexed keywords

BENDING (DEFORMATION); BOUNDARY CONDITIONS; COMPOSITE STRUCTURES; DEGREES OF FREEDOM (MECHANICS); FIBER REINFORCED METALS; FINITE ELEMENT METHOD; LAMINATED COMPOSITES; ORDINARY DIFFERENTIAL EQUATIONS; PLATES (STRUCTURAL COMPONENTS); POLYNOMIALS; SHEAR STRESS; STIFFNESS MATRIX;

LAMINATED PLATES; LOCK FREE MATERIAL; NON LINEAR OSCILLATIONS; SHEAR LOCKING;

OSCILLATIONS;

EID: 0343390418     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsvi.1999.2617     Document Type: Article

References (39)

1. ZIENKIEWICZ O. C. The Finite Element Method. 1977;McGraw-Hill, London.
2. BATHE K. J. Finite Element Procedures in Engineering Analysis. 1990;Prentice-Hall, Englewood Cliffs.
3. YANG P. C., NORRIS C. M., STAVSKY Y. Elastic wave propagation in heterogeneous plates. International Journal of Solids and Structures. 2:1966;665-684.
4. AHMED S., IRONS B. M., ZIENKIEWICZ O. C. Analysis of thick and thin structures by curved finite elements. Computational Methods in Applied Mechanics and Engineering. 50:1970;121-145.
5. ZIENKIEWICZ O. C., TAYLOR R. L., TOO J. M. Reduced integration techniques in general analysis of plates and shells. International Journal for Numerical Methods in Engineering. 3:1971;275-290.
6. PAWSEY S. F., CLOUGH R. W. Improved numerical integration of thick shell finite element. International Journal for Numerical Methods in Engineering. 3:1971;575-586.
7. HUGHES T. J. R., TAYLOR R. L., KANOKNUKULCHAI W. A simple and efficient finite element for plate bending. International Journal for Numerical Methods in Engineering. 11:1977;1529-1543.
8. PUGH E. D. L., HINTON E., ZIENKIEWICZ O. C. A study of quadrilateral plate bending elements with reduced integration. International Journal for Numerical Methods in Engineering. 12:1978;1059-1079.
9. NOOR A. K., ANDERSON C. M. Mixed isoparametric finite element model of laminated composite shells. Computational Methods in Applied Mechanics and Engineering. 11:1977;255-180.
10. LEE S. W., PIAN T. H. Improvement of plate and shell finite elements by mixed formulations. American Institute of Aeronautics and Astronautics Journal. 16:1978;29-34.
11. SPILKER R. L., MUNIR N. I. The hybrid stress model for thin plates. International Journal for Numerical Methods in Engineering. 15:1980;1239-1260.
12. AYAD R., DHATT G., BATOZ J. L. A new hybrid mixed variational approach forReissner-Mindlin plates - the MiSP model. International Journal for Numerical Methodsin Engineering. 42:1998;1149-1179.
13. HUGHES T. J. R., TEZDUYAR T. E. Finite elements based upon Mindlin plate theory, with particular reference to the four-node bilinear isoparametric elements. Journal of Applied Mechanics. 48:1981;587-596.
14. CRISFIELD M. A. A quadratic Mindlin element using shear constraints. Computers and Structures. 18:1984;833-852.
15. PRATHAP G. An optimally constrained 4-noded quadrilateral thin plate bending element. Computers and Structures. 18:1984;789-794.
16. 0continuous 4-noded cylindrical shell element. Computers and Structures. 21:1985;995-999.
17. SOMASHEKAR B. R., PRATHAP G., RAMESH BABU C. R. A field consistent four-noded laminated anisotropic plate/shell element. Computers and Structures. 25:1987;345-353.
18. HINTON E., CAMPBELL J. S. Local and global smoothening of discontinuous finite element functions using a least square method. International Journal for Numerical Methods in Engineering. 8:1974;461-480.
19. HUANG H. C., HINTON E. A nine node lagrangian plate element with enhanced shear interpolation. Engineering Computations. 1:1984;369-379.
20. REDDY J. N. Mechanics of Laminated Composite Plates - Theory and Analysis. 1997;CRC Press, New York.
21. WOINOWSKY-KRIEGER S. The effect of an axial force on the vibration of hinged bar. TRANS ASME, Journal of Applied Mechanics. 17:1950;35-36.
22. CHU H. N., HERRMAN G. Influence of large amplitude on free vibrations of rectangular elastic plates. Journal of Applied Mechanics. 23:1956;523-540.
23. WHITNEY J. M., LEISSA A. W. Analysis of heterogeneous anisotropic plates. Journal of Applied Mechanics. 36:1969;261-266.
24. SATHYAMOORTHY M. Nonlinear vibration analysis of plates. A review and survey of current development. Applied Mechanics Review. 40:1987;1553-1561.
25. SATHYAMOORTHY M. Nonlinear analysis of beams, Part I: a survey of recent advances. Shock and Vibration Digest. 14:1982;19-35.
26. SATHYAMOORTHY M. Nonlinear analysis of beams, Part II: finite element method. Shock and Vibration Digest. 14:1982;7-18.
27. SATHYAMOORTHY M. Recent research on large amplitude vibration of plates: a survey. Proceedings of 8th National Seminar on Aerospace Structures, IIT, Madras, India, 9-10 October 1998. 1998;Allied Publishers Ltd. Chennai. p. 198-213.
28. STOKER J. J. Nonlinear Vibration in Mechanical and Electrical Systems. 1950;Inter Science Publishers, New York.
29. NAYFEH A. H., MOOK D. T. Nonlinear Oscillation. 1979;John Wiley, New York.
30. SATHYAMOORTHY M. Nonlinear Analysis of Structures. 1998;CRC Press, New York.
31. SINGH G., VENKATESWARA RAO G., IYENGAR N. G. R. Large deflection behavior of shear deformable composite plates using a simple higher order theory. Composites Engineering. 3:1993;507-525.
32. SINGH G., VENKATESWARA RAO G., IYENGAR N. G. R. Analysis of nonlinear vibrations of unsymmetrically laminated composite beams. American Institute of Aeronautics and Astronautics Journal. 29:1991;1727-1735.
33. SINGH G., VENKATESWARA RAO G. Nonlinear oscillations of thick asymmetric cross-ply beams. Acta Mechanica. 127:1998;135-146.
34. HUANG S. Nonlinear vibrations of a hinged orthotropic circular plate with a concentric rigid mass. Journal of Sound and Vibration. 214:1998;873-884.
35. QAISI M. I. A power series solution for the nonlinear vibrations of beams. Journal of Sound and Vibration. 199:1997;587-594.
36. LELUNG A. Y. T., CHUI S. K. Nonlinear vibration of the von Karman plate by IHB method. Journal of Sound and Vibration. 204:1997;239-247.
37. BOGNER F. K., FOX R. L., SCHMIT L. A. The generation of inter-element compatible stiffness and mass matrices by the use of interpolation formulas. Presented at the Wright Patterson Air Force Base, Ohio Meeting on Matrix Methods in Structural Mechanics AFFDL-TR-66-80. 1996;397-443.
38. LAKSHMINARAYANA H. V., SRIDHARA MURTHY S. A shear-flexible triangular finiteelement model for laminated composite plates. International Journal for Numerical Methods in Engineering. 30:1984;591-623.
39. BHIMARADDI A. Large amplitude vibrations of imperfect unsymmetric angle-ply laminated plates. Journal of Sound and Vibration. 162:1993;457-470.