Stability of Anisotropic Laminated Rings and Long Cylinders Subjected to External Hydrostatic Pressure
Publication: Journal of Aerospace Engineering
Volume 18, Issue 3
Abstract
The problem of buckling of rings under external pressure has attracted interest since the late 1950s; however, the formulations developed, to date, to obtain the critical pressure are limited to special cases of orthotropic laminated construction. In this work, analytical and numerical treatments are carried out to provide results on the buckling of thin and moderately thick anisotropic rings and long cylinders. A generalized closed-form analytical formula for the buckling of thin anisotropic laminated rings is developed. Standard energy-based formulation and classical lamination theory are used to obtain the equilibrium equations assuming an intermediate class of deformation. The constitutive equations are statically condensed, in terms of the ring’s boundary conditions, to produce the effective axial, coupling, and flexural rigidities. In addition, a three-dimensional (3D) tube finite-element model is developed for nonlinear analysis of anisotropic laminated composite rings or long cylinders. The element accounts for prebuckling ring twist and first-order shear deformations. Fourier series expansions are used to express the in-plane and out-of-plane components of deformation and geometry at the three nodes of the cylindrical element. Isoparametric quadratic shape functions are used to interpolate the displacement field in between. Comparisons of the analytical and numerical results show excellent agreement for thin rings. Parametric studies are also conducted to address the effects of lamination, shell thickness, and initial out-of-roundness imperfection on the external buckling pressure.
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Acknowledgments
This work was sponsored by the Society of Manufacturing Engineers (SME) through Research Initiation Grant No. 991064. The additional support provided by Bradley University is also acknowledged.
References
Al-Hassani, S. T. S., Darvizeh, M., and Haftchenari, H. (1997). “An analytical study of composite tubes with various boundary conditions.” Compos. Struct., 39, 157-164.
Ambartsumyan, S. A. (1961). “Theory of anisotropic shells.” NASA Technical Translation N64–22801–22808, National Aeronautics and Space Administration, Washington, D.C.
Anastasiadis, J. S., and Simitses, G. J. (1993). “Buckling of pressure-loaded, long, shear deformable, cylindrical laminate shells.” Compos. Struct., 23, 221-231.
Brush, D. O., and Almroth, B. O. (1975). Buckling of bars, plates, and shells, McGraw-Hill, New York.
Cheng, S., and Ho, B. P. C. (1963). “Stability of heterogeneous aeolotropic cylindrical shells under combined loading.” AIAA J., 1(4).
Davis, P. J., and Rabinowitz, P. (1984). Methods of numerical integration, Academic, Orlando, Fla.
Flügge, W. (1960). Stresses in shells, Springer-Verlag, New York.
Fu, L., and Waas, A. M. (1995). “Response of thick composite rings under uniform external pressure.” Compos. Struct., 31, 325-338.
Hess, T. E. (1961). “Stability of orthotropic cylindrical shells under combined loading.” J. Am. Rocket Soc., 31(2).
Hodges, D. H., and Harursampath, D. (2002). “Inplane buckling of anisotropic rings.” Proc., 15th ASCE Engineering Mechanics Conf., (CD-ROM), ASCE, Reston, Va.
Jones, R. M. (1975). Mech. compos. mater., Hemisphere, New York.
Kardomateas, G. A. (1993). “Buckling of thick orthotropic cylinders under external pressure.” J. Appl. Mech., 60(Mar.), 195-202.
Kardomateas, G. A., and Philobos, M. S. (1995). “Buckling of thick orthotropic shells under combined external pressure and axial compression.” AIAA J., 33(Oct.), 1946-1953.
Kasagi, A., and Sridharan, S. (1993). “Buckling and postbuckling analysis of thick composite cylindrical shells under hydrostatic pressure.” Composites Eng., 3(5), 467-487.
Kasagi, A., and Sridharan, S. (1995). “Imperfection sensitivity of layered composite cylinders.” J. Eng. Mech., 121(7), 810-818.
Kyriakides, S., and Babcock, C. D. (1981). “Large deflection collapse analysis of an inelastic inextensional ring under external pressure.” Int. J. Solids Struct., 17(10), 981-993.
Lei, M. M., and Cheng, S. (1969). “Buckling of composite and homogeneous isotropic cylindrical shells under axial and radial loading.” J. Appl. Mech., Dec.
Malvern, L. E. (1969). Introduction to the mechanics of a continuous medium, Prentice Hall, Englewood Cliffs, N.J.
Ouellette, S. V., Hoa, T. S., and Sankar, T. S. (1986). “Buckling of composite cylinders under external pressure.” Polym. Compos., 7(5), 363-374.
Rasheed, H. A. (1996). “Behavior and strength of composite tubes considering delaminations and other defects.” PhD thesis, Univ. of Texas at Austin, Austin, Tex.
Rasheed, H. A. (2000). “Buckling of anisotropic composite cylindrical shells under external pressure.” Research Initiation Rep., Society of Manufacturing Engineers, Dearborn, Mich.
Rasheed, H. A., and Yousif, O. H. (2001). “Buckling of thin laminated orthotropic rings/long cylinders under external pressure.” Int. J. Struct. Stab. Dyn., 1(4), 485-507.
Simitses, G. J. (1976). An introduction to the elastic stability of structures, Prentice Hall, Englewood Cliffs, N.J., 221–231.
Simitses, G. J. (1986). “Buckling and postbuckling of imperfect cylindrical shells: A review.” Nonlinear analysis and NDE of composite material vessels and components, D. Hui, J. C. Duke, and H. Chung, eds., American Society of Mechanical Engineers, New York, 1-11.
Tennyson, R. C. (1975). “Buckling of laminated composite cylinders: A review.” Composites, 6, 17-24.
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Published In
Journal of Aerospace Engineering
Volume 18 • Issue 3 • July 2005
Pages: 129 - 138
Copyright
© ASCE.
History
Received: May 6, 2004
Accepted: Sep 13, 2004
Published online: Jul 1, 2005
Published in print: Jul 2005
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