Analysis of Laminated Anisotropic Shells of Revolution
Publication: Journal of Engineering Mechanics
Volume 113, Issue 1
Abstract
An efficient computational procedure is presented for the analysis of laminated anisotropic shells of revolution and assessing the sensitivity of their response to anisotropic (nonorthotropic) material coefficients. The analytical formulation is based on a form of the Sanders‐Budiansky shell theory, including the effects of both the transverse shear deformation and the laminated anisotropic material response. Each of the shell variables is expanded in a Fourier series in the circumferential coordinate, and a two‐field mixed finite element model is used for the discretization in the meridional direction. The three key elements of the procedure are: (1) use of mixed finite element models in the meridional direction with discontinuous stress resultants at the element interfaces; (2) operator splitting, or decomposition of the material compliance matrix of the shell into the sum of an orthotropic and nonorthotropic (anisotropic) part; and (3) application of a reduction method through the successive use of the finite element method and the classical Rayleigh‐Ritz technique. The finite element method is first used to generate a few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Rayleigh‐Ritz technique. The potential of the proposed procedure is discussed and numerical results are presented to demonstrate its effectiveness.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Budiansky, B. (1968). “Notes on nonlinear shell theory.” J. of Appl. Mech., 35(2), 393–401.
2.
Bushnell, D. (1970). “Analysis of buckling and vibration of ring‐stiffened segmented shells of revolution.” Int. J. of Solids and Structures, 6, 157–181.
3.
Cappelli, A. P., Nishimoto, T. S., and Radkowski, P. P. (1968). “The analysis of shells of revolution having arbitrary stiffness distributions.” Proceedings AIAA/ASME 9th Structures, Structural Dynamics, and Materials Conference, Palm Springs, Calif.
4.
Cohen, G. A. (1979). “FASOR—a second generation shell of revolution code.” Computers and Structures, 10, 301–309.
5.
Dong, R. G., and Dong, S. B. (1963). “Analysis of slightly anisotropic shells.” AIAA J., 1(11), 2565–2569.
6.
Gould, P. L. (1985). Finite element analysis of shells of revolution. Pitman, Marsh‐field, Mass.
7.
Grigorenko, Y. M. (1973). “Laminated isotropic and anisotropic shells of revolution with variable stiffness.” Izdatelstvo Naukova Dumka, Kiev USSR (in Russian).
8.
Gulati, S. T., and Essenburg, F. (1967). “Effects of anisotropy in axisymmetric cylindrical shells.” J. of Appl. Mech., 34, 659–666.
9.
Noor, A. K., and Stephens, W. B. (1973). “Comparison of finite difference schemes for analysis of shells of revolution.” NASA TN‐D‐7337, NASA Langley Res. Center, Hampton, Va.
10.
Noor, A. K., and Peters, J. M. (1980). “Reduced basis technique for nonlinear analysis of structures.” AIAA J., 18(4), 455–462.
11.
Noor, A. K., and Andersen, C. M. (1982). “Mixed models and reduced/selective integration displacement models for non‐linear shell analysis.” Int. J. for Num. Meth. in Eng., 18, 1429–1454.
12.
Noor, A. K., and Peters, J. M. (1983). “Mixed models and reduced/selective integration displacement models for vibration analysis of shells.” Hybrid and Mixed Finite Element Methods, S. N. Atluri, R. H. Gallagher and O. C. Zienkiewicz, Eds., John Wiley, New York, N.Y., 537–564.
13.
Noor, A. K., Andersen, C. M., and Tanner, J. A. (1984). “Mixed models and reduction techniques for large‐rotation nonlinear analysis of shells of revolution with application to tires.” NASA TP‐2343, NASA Langley Res. Center, Hampton, Va.
14.
Noor, A. K., and Peters, J. M. (1986). “Nonlinear analysis of anisotropic panels.” AIAA J., 24(9), 1545–1553.
15.
Noor, A. K., and Peters, J. M. (1986). “Analysis of laminated anisotropic shells of revolution.” Finite Element Methods for Plates and Shell Structures, Vol. 2, T. J. R. Hughes and E. Hinton, Eds., Pineridge Press, Swansea, U.K.
16.
Padovan, J., and Lestingi, J. F. (1974). “Complex numerical integration procedure for static loading of anisotropic shells of revolution.” Computers and Structures, 4, 1159–1172.
17.
Sanders, J. L. (1963). “Nonlinear theories for thin shells.” Quart. of Appl. Math., 21(1), 21–36.
18.
Schaeffer, H. G., and Ball, R. E. (1967). “Nonlinear deflections of asymmetrically loaded shells of revolutions.” Proceedings AIAA/ASME 8th Structures, Structural Dynamics and Materials Conference, Palm Springs, Calif., 732–749.
19.
Shtayerman, I. Y. (1924). “Theory of symmetrical deformation of anisotropic elastic shells.” Izvestia Kievsk. Politekh. i Sel.‐Khoz. Inst. (in Russian).
20.
Stricklin, J. A., Haisler, W. E., MacDougall, H. R., and Stebbins, F. J. (1968). “Nonlinear analysis of shells of revolution by the matrix displacement method.” AIAA J., 6(12), 2306–2317.
21.
Vasilenko, A. T., and Golub, G. P. (1983). “Determination of the stressed state of anisotropic shells of revolution with allowance for transverse shear.” Prikladnaia Mekhanika 19, 21–26 (in Russian).
22.
Wunderlich, W., Cramer, H., and Obrecht, H. (1985). “Application of ring elements in the nonlinear analysis of shells of revolution under nonaxisymmetric loading.” Comp. Meth. in Appl. Mech. and Eng., 51, 259–275.
Information & Authors
Information
Published In
Copyright
Copyright © 1987 ASCE.
History
Published online: Jan 1, 1987
Published in print: Jan 1987
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.