Exact Solutions of Moderately Thick Laminated Shells
Publication: Journal of Engineering Mechanics
Volume 110, Issue 5
Abstract
An extension of the Sanders shell theory for doubly curved shells to a shear deformation theory of laminated shells is presented. The theory accounts for transverse shear strains and rotation about the normal to the shell midsurface. Exact solutions of the equations are presented for simply supported, doubly curved, cross‐ply laminated shells under sinusoidal, uniformly distributed, and concentrated point load at the center. Fundamental frequencies of cross‐ply laminated shells are also presented. The exact solutions presented herein for laminated composite shells should serve as bench mark solutions for future comparisons.
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References
1.
Ambartsumyan, S. A., Theory of Anisotropic Shells, Moscow, 1961; English translation, NASA TT F 118, May, 1964.
2.
Ambartsumyan, S. A., “Calculation of Laminated Anisotropic Shells,” Izvestiia Akademiia Nauk Armenskoi SSR, Ser. Fiz. Mat. Est. Tekh. Nauk., Vol. 6, No. 3, 1953, p. 15.
3.
Bert, C. W., and Francis, P. H., “Composite Material Mechanics: Structural Mechanics,” AIAA Journal, Vol. 12, No. 9, 1974, pp. 1173–1186.
4.
Bert, C. W., “Analysis of Shells,” Structural Design and Analysis, Part I, C. C. Chamis, ed., Vol. 7of Composite Materials, L. J. Broutman and R. H. Krock, eds., John Wiley and Sons, Inc., New York, N.Y., 1974, pp. 207–258.
5.
Bert, C. W., and Chen, T. L. C., “Effect of Shear Deformation on Vibration of Antisymmetric Angle‐Ply Laminated Rectangular Plates,” International Journal of Solids and Structures, Vol. 14, 1978, pp. 465–473.
6.
Bert, C. W., and Kumar, M., “Vibration of Cylindrical Shells of Bimodulus Composite Materials,” Journal of Sound and Vibration, Vol. 81, No. 1, 1982, pp. 107–121.
7.
Bert, C. W., and Reddy, V. S., “Cylindrical Shells of Bimodulus Material,” Journal of the Engineering Mechanics Division, ASCE, Vol. 8, No. EM5, 1982, pp. 675–688.
8.
Cheng, S., and Ho, B. P., “Stability of Heterogeneous Aelotropoic Cylindrical Shells Under Combined Loading,” AIAA Journal, Vol. 1, No. 4, 1963, pp. 892–898.
9.
Dong, S. B., Pister, K. S., and Taylor, R. L., “On the Theory of Laminated Anisotropic Shells and Plates,” Journal of Aerospace Sciences, Vol. 29, 1962, pp. 969–975.
10.
Donnell, L. H., “Stability of Thin Walled Tubes in Torsion,” NACA Report 479, 1933.
11.
Flugge, W., Stresses in Shells, Julius Springer, Berlin, Germany, 1960.
12.
Gulati, S. T., and Essenberg, F., “Effects of Anisotropy in Axisymmetric Cylindrical Shells,” Journal of Applied Mechanics, Vol. 34, 1967, pp. 650–666.
13.
Hsu, Y. S., Reddy, J. N., and Bert, C. W., “Thermoelasticity of Circular Cylindrical Shells Laminated of Bimodulus Composite Materials,” Journal of Thermal Stresses, Vol. 4, 1981, pp. 155–177.
14.
Kraus, H., Thin Elastic Shells, John Wiley and Sons, Inc., New York, N.Y., 1967.
15.
Love, A. E. H., “On the Small Free Vibrations and Deformations of the Elastic Shells,” Philosophical Transactions of the Royal Society, (London), Ser. A, Vol. 17, 1888, pp. 491–546.
16.
Naghdi, P. M., “A Survey of Recent Progress in the Theory of Elastic Shells,” Applied Mechanics Reviews, Vol. 9, No. 9, 1956, pp. 365–368.
17.
Reddy, J. N., and Chao, W. C., “A Comparison of Closed‐Form and Finite Element Solutions of Thick, Laminated, Anisotropic Rectangular Plates,” Nuclear Engineering and Design, Vol. 64, 1981, pp. 153–167.
18.
Sanders, J. L., Jr., “An Improved First‐Approximation Theory for Thin Shells,” NASA Technical Report R‐24, 1959.
19.
Stavsky, Y., “Thermoelasticity of Heterogeneous Aeolotropic Plates,” Journal of the Engineering Mechanics Division, ASCE, Vol. 89, No. EM2, 1963, pp. 89–105.
20.
Vlasov, V. Z., General Theory of Shells and Its Applications in Engineering (Translation of Obshchaya teoriya obolocheck i yeye prilozheniya v tekhnike), NASA TT F‐99, National Aeronautics and Space Administration, Washington, D.C., 1964.
21.
Whitney, J. M., and Leissa, A. W., “Analysis of Heterogeneous Anisotropic Plates,” Journal of Applied Mechanics, Vol. 36, 1969, pp. 261–266.
22.
Whitney, J. M., and Pagano, N. J., “Shear Deformation in Heterogeneous Anisotropic Plates,” Journal of Applied Mechanics, Vol. 37, 1970, pp. 1031–1036.
23.
Whitney, J. M., and Sun, C. T., “A Higher Order Theory for Extensional Motion of Laminated Anisotropic Shells and Plates,” Journal of Sound and Vibration, Vol. 30, 1973, p. 85.
24.
Whitney, J. M., and Sun, C. T., “A Refined Theory for Laminated Anisotropic Cylindrical Shells,” Journal of Applied Mechanics, Vol. 41, 1974, pp. 471–476.
25.
Widera, G. E. O., and Chung, S. W., “A Theory for Nonhomogeneous Anisotropic Cylindrical Shells,” Journal of Applied Mathematics & Physics(ZAMP), Vol. 21, 1970, pp. 378–399.
26.
Widera, G. E. O., and Logan, D. L., “Refined Theories for Nonhomogeneous Anisotropic Cylindrical Shells: Part I—Derivation,” Journal of the Engineering Mechanics Division, ASCE, Vol. 106, No. EM6, 1980, pp. 1053–1074.
27.
Yang, T. Y., “High Order Rectangular Shallow Shell Finite Element,” Journal of the Engineering Mechanics Division, ASCE, Vol. 99, No. EM1, 1973, pp. 57–181.
28.
Zukas, J. A., and Vinson, J. R., “Laminated Transversely Isotropic Cylindrical Shells,” Journal of Applied Mechanics, Vol. 38, 1971, pp. 400–407.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 110 • Issue 5 • May 1984
Pages: 794 - 809
Copyright
Copyright © 1984 ASCE.
History
Published online: May 1, 1984
Published in print: May 1984
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