Free-vibration analysis of plates and shells with a nine-node assumed natural degenerated shell element

Journal of Sound and Vibration

Volumn 241, Issue 4, 2001, Pages 605-633

  Lee, S J ^a   Han, S E ^b  

^a Korea Atomic Energy Research Institute   (South Korea)

^b Inha University   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; FINITE ELEMENT METHOD; INTEGRATION; ITERATIVE METHODS; PLATES (STRUCTURAL COMPONENTS); SHEAR DEFORMATION; SHELLS (STRUCTURES); STIFFNESS MATRIX; STRAIN;

FREE VIBRATION ANALYSIS; SHELL FINITE ELEMENT FORMULATION;

VIBRATIONS (MECHANICAL);

EID: 0035810055     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsvi.2000.3313     Document Type: Article

References (39)

1. LOVE A. E. H. The small vibrations and deformations of thin elastic shell. Philosophical Transactions of the Royal Society. 179:1888;527-546.
2. L. H. DONELL, 1933, NASA Report 479, Stability of thin-walled tubes under torsion.
3. LEISSA A. W. Vibrations of shells. NASA PA-288, Washington, DC. 1973.
4. QATU M. S. Review of shallow shell vibration research. Shock Vibration Digest. 24:1992;3-15.
5. LIEW K. M., LIM C. W., KITIPORNCHAI S. Vibration of shallow shells: a review with bibliography. Applied Mechanics Reviews. 50:1997;431-444.
6. ADINI A. Analysis of shell structures by the finite element methods. Ph.D Dissertation, University of California, Berkeley. 1961.
7. GALLAGHER R. H. Shell elements. Proceedings of the World of the conference on Finite element methods in structural mechanics, Bournemouth. 1975.
8. AHMAD S., IRONS B. M., ZIENKIEWICZ O. C. Analysis of thick and thin shell structures by curved finite elements. International Journal of Numerical Methods in Engineering. 2:1970;419-451.
9. W. P. DOHERTY, E. J. WILSON, R. L. TAYLOR, 1969, UC-SESM Report No. 69-3, Department of Civil Engineering, University of California, Berkeley, Stress analysis of axisymmetric solids utilizing higher order quadrilateral finite element.
10. ZIENKIEWICZ O. C., TAYLOR R. L., TOO J. M. Reduced integration technique in general analysis of plates and shells. International Journal of Numerical Methods in Engineering. 3:1971;275-290.
11. BATHE K. J., DVORKIN E. N. A four-node plate bending element based on Mindlin-Reissner plate theory and a mixed formulation. International Journal of Numerical Methods in Engineering (Short Communication). 21:1985;367-383.
12. BELYTSCHKO T., WONG B. L., STOLARSKI H. Assumed strain stabilization procedure for the 9-node Lagrangian shell element. International Journal of Numerical Methods in Engineering. 28:1989;385-414.
13. LIEW K. M. Research on thick plate vibration: a literature survey. Journal of Sound and Vibration. 180:1995;163-176.
14. HUGHES T. J. R. The Finite Element Method - Linear Static and Dynamic Finite Element Analysis. 1987;Prentice-Hall, Englewood Cliffs.
15. BATHE K. J. Finite Element Procedures in Engineering Analysis. 1982;Prentice-Hall, Englewood Cliffs.
16. ZIENKIEWICZ O. C., TAYLOR R. L. The Finite Element Method. 1989;McGraw-Hill, London.
17. KANOK-NUKULCHAI W. A simple and efficient finite element for general shell analysis. International Journal of Numerical Methods in Engineering. 14:1979;179-200.
18. LEE S. J., KANOK-NUKULCHAI W. A nine-node assumed strain finite element for large-deformation analysis of laminated shells. International Journal of Numerical Methods in Engineering. 4:1998;777-798.
19. HUANG H. C., HINTON E. A new nine-node degenerated shell element with enhanced membrane and shear interpolation. International Journal of Numerical Methods in Engineering. 22:1986;73-92.
20. LEE S. J., KIM Y. B. Finite element analysis of laminated plates with assumed strain method. Journal of the Architectural Institute of Korea. 10:1994;181-188.
21. LEISSA A. W. The free vibration of rectangular plates. Journal of Sound and Vibration. 31:1973;257-293.
22. JANABI B. S. AI., HINTON E. A study of the free vibrations of square plates with various edge conditions. Hinton E. Numerical Methods and Software for Dynamic Analysis of Plates and Shells. 1988;167-204 Pineridge Press, Swansea.
23. SRINIVAS S., JOGA RAO C. V., RAO A. K. An exact analysis for vibration of simply supported homogeneous and laminated, thick rectangular plates. Journal of Sound and Vibration. 12:1970;187-199.
24. REDDY J. N., PHAN N. D. Stability and vibration of isotropic and laminated plates according to a higher-order shear deformation theory. Journal of Sound and Vibration. 98:1985;157-170.
25. HINTON E., VUKSANOVIC DJ. Closed form solutions for dynamic analysis of simply supported Mindlin plates. Hinton E. Numerical Methods and Software for Dynamic Analysis of Plates and Shells. 1988;1-47 Pineridge Press, Swansea.
26. REISSNER E. The effect of transverse shear deformation on the bending of elastic plate. ASME Journal of Applied Mechanics. 12:1945;69-76.
27. DAWE D. J., ROUFAEIL O. L. Rayleigh-Ritz vibration analysis of Mindlin plates. Journal of Sound and Vibration. 69:1980;345-359.
28. DAWE D. J. Finite strip models for vibration of Mindlin plates. Journal of Sound and Vibration. 59:1978;441-452.
29. HINTON E., VUKSANOVIC D. J., HUANG H. C. Finite element free vibration and bucking analysis of initially stesses Mindlin plates. Hinton E. Numerical Methods and Software for Dynamic Analysis of Plates and Shells. 1988;93-166 Pineridge Press, Swansea.
30. LEISSA A. W. Vibration of plates. NASA SP-160, Washington, DC. 1969.
31. LIEW K. M. Use of two-dimensional orthogonal polynomials for vibration analysis of curcular and elliptical plates. Journal of Sound and Vibration. 154:1992;261-269.
32. ABAQUS Theory and User Manuals, Hibbit, Karlson and Sorensen, Inc.
33. LIEW K. M. Vibration behaviour of doubly curved shallow shells of curvilinear planform. Journal of Engineering Mechanics. 121:1995;1277-1283.
34. DEB NATH J. M. Dynamics of rectangular curved plates. Ph.D. Thesis, University of Southampton. 1969.
35. PETYT M. Vibration of curved plates. Journal of Sound and Vibration. 15:1971;381-395.
36. LIM C. W., LIEW K. M. A higher order theory for vibration of shear deformable cylindrical shallow shells. International Journal of Mechanical Sciences. 37:1995;277-295.
37. OLSON M. D. Dynamic analysis of shallow shells with a doubly-curved triangular finite element. Journal of Sound and Vibration. 3:1971;299-318.
38. LEE J. K., LEISSA A. W., WANG A. J. Vibrations of cantilevered shallow cylindrical shells of rectangular planform. Journal of Sound and Vibration. 78:1981;311-328.
39. LIM C. W., LIEW K. M. A ph-z Ritz formulation for flexural vibration of shallow cylindrical shell of rectangular planform. Journal of Sound and Vibration. 173:1994;343-375.