Elastic Buckling of Multilayered Anisotropic Conical Shells
Publication: Journal of Aerospace Engineering
Volume 14, Issue 1
Abstract
On the basis of 3D elasticity, asymptotic solutions for buckling analysis of multilayered anisotropic conical shells under axial compression are presented. By means of proper nondimensionalization, asymptotic expansion, and successive integration, the classical shell theory is derived as a first-order approximation to the 3D theory. Because the governing equations for various orders consist of partial differential equations with variable coefficients, the use of analytical techniques is restricted. The method of differential quadrature is adopted in the present study. The modifications of the buckling loads and associated buckling modes can be determined in a consistent and hierarchic manner by considering the solvability and normalization conditions for various orders. The critical loads of cross-ply conical shells with simply supported–simply supported boundary conditions are studied to demonstrate the performance of the present asymptotic theory.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Baruch, M., Harari, O., and Singer, J. ( 1970). “Low buckling loads of axially compressed conical shells.” J. Appl. Mech., 37, 384–392.
2.
Bellman, R., and Casti, J. ( 1971). “Differential quadrature and long-term integration.” J. Math. Anal. Appl., 34, 235–238.
3.
Bellman, R., Kashef, B. G., and Casti, J. ( 1972). “Differential quadrature: A technique for the rapid solution of nonlinear partial differential equations.” J. Comp. Phys., 10, 40–52.
4.
Bert, C. W., and Malik, M. ( 1996). “Differential quadrature method in computational mechanics: A review.” Appl. Mech. Rev., 49, 1–27.
5.
Bert, C. W., and Malik, M. ( 1997). “Differential quadrature: A powerful new technique for analysis of composite structures.” Compos. Struct., 39, 179–189.
6.
Brush, D. O., and Almroth, B. O. ( 1975). Buckling of bars, plates, and shells, McGraw-Hill, New York.
7.
Du, H., Lim, M. K., and Lin, R. M. ( 1994). “Application of generalized differential quadrature method to structural problems.” Int. J. Numer. Methods Engrg., 37, 1881–1896.
8.
Jones, R. M. ( 1975). Mechanics of composite materials, McGraw-Hill, New York.
9.
Kardomateas, G. A. ( 1993a). “Buckling of thick orthotropic cylindrical shells under external pressure.” J. Appl. Mech., 60, 195–202.
10.
Kardomateas, G. A. ( 1993b). “Stability loss in thick transversely isotropic cylindrical shells under axial compression.” J. Appl. Mech., 60, 506–512.
11.
Leissa, A. W. ( 1987). “A review of laminates composite plate buckling.” Appl. Mech. Rev., 40, 575–591.
12.
Leissa, A. W. ( 1995). “Buckling and postbuckling theory for laminated composite plates.” Buckling and postbuckling of composite plates, G. J. Turvey and I. H. Marshall, eds., Chapman & Hall, Glasgow, U.K.
13.
Nayfeh, A. H. ( 1993). Introduction to perturbation techniques, Wiley, New York.
14.
Saada, A. S. ( 1974). Elasticity theory and applications, Pergamon, New York.
15.
Seide, P. ( 1956). “Axisymmetrical buckling of circular cones under axial compression.” J. Appl. Mech., 23, 626–628.
16.
Shu, C. ( 1996). “Free vibration analysis of composite laminated conical shells by generalized differential quadrature.” J. Sound Vib., 194, 587–604.
17.
Shu, C., and Du, H. ( 1997). “Free vibration analysis of laminated composite cylindrical shells by DQM.” Compos., Part B, 28, 267–274.
18.
Simitses, G. J. ( 1986). “Buckling and postbuckling of imperfect cylindrical shells: A review.” Appl. Mech. Rev., 39, 1517–1524.
19.
Simitses, G. J. ( 1996). “Buckling of moderately thick cylindrical shells: A review.” Compos., Part B, 27, 581–587.
20.
Soedel, W. ( 1993). Vibrations of shells and plates, Marcel Dekker, New York.
21.
Tennyson, R. C. ( 1975). “Buckling of laminated composite cylinders: A review.” Compos., 6, 17–29.
22.
Tong, L., and Wang, T. K. ( 1992). “Simple solutions for buckling of laminated conical shells.” Int. J. Mech. Sci., 34, 93–111.
23.
Tong, L., and Wang, T. K. ( 1993). “Buckling analysis of laminated composite conical shells.” Compos. Sci. Technol., 47, 57–63.
24.
Wu, C. P., and Hung, Y. C. ( 1999). “Asymptotic theory of laminated circular conical shells.” Int. J. Engrg. Sci., 37, 977–1005.
25.
Ye, J., and Soldatos, K. P. ( 1995). “Three-dimensional buckling analysis of laminated composite hollow cylinders and cylindrical panels.” Int. J. Solids and Struct., 32, 1949–1962.
Information & Authors
Information
Published In
History
Received: Mar 28, 2000
Published online: Jan 1, 2001
Published in print: Jan 2001
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.