Hostname: page-component-7bb8b95d7b-fmk2r Total loading time: 0 Render date: 2024-10-06T08:42:47.886Z Has data issue: false hasContentIssue false
  • English
  • Français

Free vibration of laminated beams and stiffened plates using a high-order element

Published online by Cambridge University Press:  04 July 2016

Abhijit Mukherjee
Abhijit Mukherjee*
Affiliation:
Institute for Computer Applications, University of Stuttgart, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

Free vibration analysis of laminated composite beams, plates and stiffened plates using the finite element method has been presented. To give due importance to the shear deformation in composite materials, a high-order element which considers the quadratic variation of shear strain along the thickness of the element has been developed. The element has been developed using the quadratic isoparametric shape functions. Therefore, it can accommodate curved boundaries. Moreover, the stiffener element can have an arbitrary planform and it need not pass through any nodal point. The stiffener element has been developed in such a fashion to make the mesh division free from the location of the stiffener. This is extremely advantageous for optimisation of the path of the stiffener in a stiffened plated structure, while it is not necessary to modify the mesh division whenever the stiffener path is modified. Two different shape functions — the eight-node Serendipity and the nine-node Lagrangian — have been employed and a comparison between their performances has been presented. Two schemes for the generation of mass matrix, namely the lumped mass scheme and the consistent mass scheme, have been developed. The elements have been implemented in the ASKA element library and they can be used along with any standard ASKA element.

Type
Research Article
Information
The Aeronautical Journal , Volume 95 , Issue 944 , April 1991 , pp. 124 - 131
Copyright
Copyright © Royal Aeronautical Society 1991 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

p1

Present address: Department of Civil Engineering, Indian Institute of Technology, Bombay, India.

References

1. Kapania, R. K. and Raciti, S. Recent advances in analysis of laminated beams and plates, Part I: Shear effects and buckling, AIAA J, 1989, 27, pp 923–924.Google Scholar
2. Kapania, R. K. and Raciti, S. Recent advances in analysis of laminated beams and plates, Part II: Vibrations and wave propagation, AIAA J, 1989, 27, pp 935–946.Google Scholar
3. Lekhnitskii, S. G. Theory of elasticity of an anisotropic body, San Francisco Calif. 1963, Holdenday.Google Scholar
4. Abarcar, R. B. and Cunniff, P. F. The vibration of cantilever beams of fibre reinforced material, J Compos Mater, 1972, 6, pp 504–517.Google Scholar
5. Teoh, L. S. and Huang, C. C. The vibration of beams of fibre reinforced material, J Sound Vibr, 1977, 51, pp 467–473.Google Scholar
6. Murty, A. V. K. and Shimpi, R. P. Vibration of laminated beams, J Sound Vibr, 1981, 41, pp 433–449.Google Scholar
7. Chen, A. T. and Yang, T. Y. Static and dynamic formulation of a symmetrically laminated beam finite element for a micro computer, J Compos Mater, 1985, 19, pp 459–475.Google Scholar
8. Kapania, R. K. and Raciti, S. Nonlinear vibrations of unsymmetrically laminated beams, AIAA J, 1989, 27, pp 201–210.Google Scholar
9. Bhimaraddi, A., Carr, A. J. and Moss, P.J. Generalized finite element analysis of laminated curved beams with constant curvature, Comput Struct, 1989, 31, pp 309–317.Google Scholar
10. Bhimaraddi, A. Generalized analysis of shear deformable rings and curved beams, J Solids Struct, 1988, 24, pp 363–373.Google Scholar
11. Rhodes, M. D., William, J. G. and Starnes, J. H. Effect of Low Velocity Impact Damage on the Compressive Strength of Graphite-Epoxy Hat-Stiffened Panels, 1977, NASA TN D-8411.Google Scholar
12. William, J. C., Anderson, M. S., Rhodes, M. D., Starnes, J. H. and Stroud, W. J. Recent development of the design, testing, and impact damage tolerance of stiffened composite panels, 1979, NASA TM 80077.Google Scholar
13. Hyer, M. W., Loup, D. C. and Starnes, J. H. Stiffener/skin interactions in pressure loaded composite panels, AIAA J, 1990, 28, pp 532–537.Google Scholar
14. Venkatesh, A. and Rao, K. P. A laminated anisotropic curved beam and shell stiffening finite element, Comput Struct, 1982, 15, pp 197–201.Google Scholar
15. Venkatesh, A. and Rao, K. P. Analysis of laminated shells with laminated stiffeners using rectangular finite elements, Comp Meth Appl Mech Eng, 1983, 38, pp 255–272.Google Scholar
16. Venkatesh, A. and Rao, K. P. Analysis of laminated shells of revolution with laminated stiffeners using a doubly curved quadrilateral finite element, Comput Struct, 1985, 20, pp 669–682.Google Scholar
17. Liao, C. L. and Reddy, J. N. Continuum-based stiffened composite shell element for geometrically nonlinear analysis, AIAA J, 1989, 27, pp 95–101.Google Scholar
18. Liao, C. L. and Reddy, J. N. Analysis of anisotropic, stiffened composite laminates using a continuum-based shell element, Comput Struct, 1990, 34, pp 805–815.Google Scholar
19. Bhimaraddi, A. Static and transient response of rectangular plates, Thin Walled Struct, 1987, 5, pp 125–143.Google Scholar
20. Bhimaraddi, A. Static and transient response of cylindrical shells, Thin Walled Struct, 1987, 5, pp 157–179.Google Scholar
21. Bhimaraddi, A., Carr, A. J. and Moss, P. J. Finite element analysis of laminated shells of revolution with laminated stiffeners, Comput Struct, 1989, 33, pp 295–305.Google Scholar
22. Attaf, B. and Hollaway, L. Vibrational analyses of stiffened and unstiffened composite plates subjected to in-plane loads, Composites, 1990, 21, pp 117–126.Google Scholar
23. Mukherjee, A. Free vibration of laminated plates using a high-order element, Comput Struct (in press).Google Scholar
24. Rock, T. A. and Hinton, E. A finite element method for the free vibration of plates allowing for transverse shear deformation, Comput Struct, 1976, 6, pp 37–44.Google Scholar