Elliptical and Circular Cylindrical Sandwich Shells with Different Facings

Abstract

The Sanders-type theory of elliptical sandwich shells with different facings is formulated. The governing equations account for transverse shear strains and for rotations about the normal to the middle surface of the shell. The constitutive equations correspond to a sandwich shell where each facing is formed of an even number of regular symmetrically laminated layers. Accordingly, the matrix of extensional, coupling and bending stiffnesses is fully populated, except for the elements A₁₆ and A₂₆ that are equal to zero. In addition, a geometrically nonlinear formulation is presented for an elliptical facing resting on an elastic foundation, based on the Sanders nonlinear shell theory. In this formulation, the rotations about the normal to the middle surface as well as transverse shear strains are disregarded. Both the governing equations for the sandwich shell and the nonlinear solution for a facing are reduced to the corresponding results for a circular cylindrical shell if the radius of curvature of the shell is constant.

Numerical examples are presented for the problem of buckling of a long cylindrical shell subjected to a lateral pressure. This solution, developed by using the energy method, illustrates the penalty involved in using different facings, which may nevertheless be necessary to improve the design by reinforcing the facing exposed to low-velocity impact and other loads.

Get full access to this article

View all access options for this article.

References

1. Vafakos, W. P. , Romano, F. and Kempner, J. , 1962, "Clamped Short Oval Cylindrical Shells Under Hydrostatic Pressure," Journal of the Aerospace Sciences, Vol. 29, pp. 1347-1357.

2. Vafakos, W. P. , Nissel, N. and Kempner, J. , 1964, "Energy Solutions for Simply-Supported Oval Shells," AIAA Journal, Vol. 2, pp. 555-557.

3. Vafakos, W. P. , Nissel, N. and Kempner, J. , 1966, "Pressurized Oval Cylinders with Closely Spaced Rings," AIAA Journal, Vol. 4, pp. 338-345.

4. Nissel, N. and Vafakos, W. P. , 1968, "Assymptotic Solution for Short Ring-Reinforced Oval Cylinders," AIAA Journal, Vol. 6, pp. 133-140.

5. Kempner, J. and Chen, Y.-N. , 1965, "Large Deflections of an Axially Compressed Oval Cylindrical Shell," Proceedings of the XI International Congress of Applied Mechanics, Munich, Germany, (1964), Springer-Verlag, Berlin, pp. 299-305.

6. Kempner, J. and Chen, Y.-N. , 1967, "Buckling and Postbuckling of an Axially Compressed Oval Cylindrical Shell," Proceedings of the Symposium on the Theory of Shells (L.H. Donnell 7Oth Anniversary Volume), Houston, pp. 139-183.

7. Sewall, J. L. and Pusey. C. G. 1971, "Vibration Study of Clamped-Free Elliptical Cylindrical Shells," AIAM Journal, Vol. 9, pp. 1004-1011.

8. Daugherty, R. L. and Vinson, J. R. 1969, "Asymptotic Solution for Noncircular Cylinders of Pyrolitic Graphite," Developments in Mechanics, Proceedings of the 11th Midwestern Conference, Vol. 5, pp. 563-576.

9. Grigorenko, Ya. M. and Vasilenko, A. T. 1992, Problems of Statics of Anisotropic Heterogeneous Shells, Nauka, Moscow. In Russian.

10.

10. Meyers, C. A. and Hyer, M. W. , 1997, "Response of Elliptical Composite Cylinders to Internal Pressure Loading," Mechanics of womposite Materials and Structures. Vol. 4, pp. 317-343.

11.

11. Meyers, C. A. and Hyer, M. W. , 2000, "Response of Elliptical Composite Cylinders to Axial Compression Loading," Mechanics of Composite Materials and Structures. In press.

12.

12. Sanders, J. L., Jr. , 1959, An Improved First Approximation Theory for Thin Shells, NACA Report 24, Washington, D.C.

13.

13. Birman, V. and Simitses, G. J. , 1998, "Theory of Box-Type Sandwich Shells with Dissimilar Facings Subjected to Thermomechanical Loads," AIAA Journal, Vol. 38, pp. 362-367.

14.

14. Reissner, E. , 1945, "The Effect of Transverse Shear Deformation on the Bending of Elastic Plate," ASME Journal of Applied Mechanics, Vol. 12, pp. A69-A77.

15.

15. Mindlin, R. D. , 1951, "Influence of Rotatory Inertia and Shear on Flexural Motions of Isotropic Elastic Plates," ASME Journal of Applied Mechanics, Vol. 18, pp. 31-38.

16.

16. Gordaninejad, F. and Bert, C. W. , 1989, "A New Theory for Bending of Thick Sandwich Beams," International Journal of Mechanical Sciences, Vol. 31, pp. 925-934.

17.

17. Whitney, J. M. , 1973, "Shear Correction Factors for Orthotropic Laminates Under Static Load," ASME Journal of Applied Mechanics, Vol. 40, pp.302-304.

18.

18. Yu, Y.-Y. , 1959, "Simple Thickness Shear Models of Vibration of Infinite Sandwich Plates," ASME Journal of Applied Mechanics, Vol. 26, pp. 679-681.

19.

19. Greenberg, J. B. and Stavsky, Y. , 1980, "Vibrations of Axially Compressed Laminated Orthotropic Cylindrical Shells, Including Shear Deformation," Acta Mechanica, Vol. 37, pp. 13-28.

20.

20. Marguerre, K. , 1951, Stability of the Cylindrical Shell of Variable Curvature, NASA TM 1302.

21.

21. Simitses, G. J. , Shaw, D. and Sheinman, I. , 1985, "Stability of Cylindrical Shells by Various Nonlinear Theories," ZAMM, Vol. 65, pp. 159-166.

22.

22. Noor, A. K. , Burton, W. S. and Bert, C. W. , 1996, "Computational Models for Sandwich Panels and Shells," Applied Mechanics Reviews, Vol. 49, pp. 155-199.

23.

23. Koiter, W. T. , 1963, "Elastic Stability and Postbuckling Behavior," Non-Linear Problems, Langer, R.E. , ed., University of Wisconsin Press, Madison, Wisconsin.

24.

24. Stein, M., 1988, "Postbuckling of Eccentric Open-Section Stiffened Composite Panels" AIAA Paper 88-2215 (Collection of Technical Papers of the 29th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference, Part 1, pp. 57-61, AIAA, Washington, D.C.)

25.

25. Palazotto, A. N. , 1995, "Instability of Composite Panels," Buckling and Post buckling of Composite Plates, Turvey, G. J. and Marshall, I. H. , eds., Chapman & Hall, London, pp. 366-389.

26.

26. Paydar, N. and Libove, C. , 1986, "Stress Analysis of Sandwich Plates with Unidirectional Thickness Variation," ASME Paper 86-WA/APM-40.

27.

27. Timoshenko, S. P. and Gere J. M. , 1981, Theory of Elastic Stability, Second Edition, McGraw-Hill, New York.