Stress, Vibration, and Buckling of Multilayered Cylinders
Publication: Journal of Structural Engineering
Volume 115, Issue 1
Abstract
An efficient computational procedure is presented for reducing the cost of the stress, free vibration, and buckling analyses of multilayered composite cylinders. The analytical formulation is based on the linear three‐dimensional theory of elasticity. The cylinders are assumed to have simply supported curved edges, and the fibers of the different layers are either in the circumferential or longitudinal direction. The fundamental unknowns consist of the six stress components and the three displacement components of the cylinder. Each of the variables is expressed in terms of a double Fourier series in the longitudinal and circumferential coordinates, and a two‐field mixed finite element model is used for the discretization in the thickness direction. The cylinder response associated with a range of Fourier harmonics in the longitudinal and circumferential directions is approximated by a linear combination of a few global approximation vectors, which are generated at particular values of the Fourier harmonics, within that range. The full equations of the finite element model are solved for only a single pair of Fourier harmonics, and the response corresponding to the other Fourier harmonics is generated using a reduced system of equations with considerably fewer degrees of freedom.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Armenakas, A. E., Gazis, D. C., and Herrmann, G. (1969). Vibrations of circular cylindrical shells. Pergamon Press, Elmsford, N.Y.
2.
Chou, F. H., and Achenbach, J. D. (1972). “Three‐dimensional vibrations of orthotopic cylinders.” J. Engrg. Mech. Div., ASCE, 98(EM4), 813–822.
3.
Concus, P., Golub, G., and O'Leary, D. (1976). “A generalized conjugate gradient method for the numerical solution of elliptic partial differential equations.” Sparse matrix computations, J. Bunch and D. Rose, eds., Academic Press, Orlando, Fla., 309–322.
4.
Cullum, J. K. (1985). Lanczos algorithms for large symmetric eigenvalue computations, Vol. 1: Theory, progress in scientific computing. Birkhauser, Cambridge, Mass.
5.
Dong, S. B. (1972). “Studies relating to the structural dynamic behavior of laminated plates and shells.” UCLA‐ENG‐7236, University of California, Los Angeles, Calif.
6.
Greenbaum, A. (1979). “Comparison of splittings used with the conjugate gradient algorithm.” Nutnerische Mathematik, 33(2), 181–194.
7.
MacNeal, R. H. (1977). “The solution of large structural dynamic problems.” Proc., Symp. on Applications of Computer Methods in Engineering, University of Southern California, Los Angeles, Calif., 77–86.
8.
Mirsky, I. (1964). “Vibrations of orthotropic, thick cylindrical shells.” J. Acoust. Soc. Am., 36(1), 41–51.
9.
Mirsky, I. (1965a). “Wave propagation in transversely isotropic circular cylinders, Part I: Theory.” J. Acoust. Soc. Am., 37(6), 1016–1021.
10.
Mirsky, I. (1965b). “Wave propagation in transversely isotropic circular cylinders, Part II: Numerical results.” J. Acoust. Soc. Am., 37(6), 1022–1026.
11.
Noor, A. K., and Peters, J. M. (1987). “Preconditioned conjugate gradient technique for the analysis of symmetric anisotropic structures.” Int. J. Numer. Methods Engrg., 24(11), 2057–2070.
12.
Noor, A. K., and Rarig, P. L. (1974). “Three‐dimensional solutions of laminated cylinders.” Comput. Methods Appl. Mech. Eng., 3(3), 319–334.
13.
Nour‐Omid, B., and Clough, R. W. (1984). “Dynamic analysis of structures using Lanczos coordinates.” Earthquake Eng. Struct. Dyn., 12(4), 565–577.
14.
Parlett, B. N. (1980). The symmetric eigenvalue problem. Prentice‐Hall, Englewood Cliffs, N.Y.
15.
Wilson, E. L., Yuan, M. W., and Dickens, J. (1982). “Dynamic analysis by direct superposition of Ritz vectors.” Earthquake Eng. Struct. Dyn., 10(6), 813–821.
Information & Authors
Information
Published In
Copyright
Copyright © 1989 ASCE.
History
Published online: Jan 1, 1989
Published in print: Jan 1989
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.