Formulations and computational procedures are presented for the finite element analysis of laminated anisotropic composite thin shells including imperfections. The derivations of the nonlinear geometric element stiffness matrices were based on the total Lagrangian description. A 48 degree-of-freedom (d.o.f.) general curved shell element with arbitrary distribution of curvatures was used to model the shell middle- surface. Numerical results include the large deflection behavior of a variety of perfect plate and shell examples; buckling of a spherical shell with an axially symmetric im perfection ; and buckling of a cylindrical panel using measured initial transverse im perfections. A good comparison with existing results is obtained.
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References
1.
Kapania, R.K. and Yang, T.Y., "Formulations of an Imperfect Quadrilateral Doubly Churved Shell Element for Post-Buckling Analysis,"AIAA Journal (1986).
2.
Noor, A.K. and Hartley, S.J., "Nonlinear Shell Analysis via Mixed Isoparametric Elements,"Computers and Structures, Vol. 7, p. 615 (1977 ).
3.
Chang, T.Y. and Sawamiphakdi, K. , "Large Deformation Analysis of Laminated Shells by Finite Element Method,"Computers and Structures , Vol. 13, p. 331 (1981).
4.
Reddy, J.N. and Chandrashekhara, K., "Nonlinear Analysis of Laminated Shells Including Transverse Shear Strains,"AIAA Journal, Synoptic paper No. J14578, to appear (1984).
5.
Chia, C.Y., Nonlinear Analysis of Plates, McGraw-Hill , New York (1980).
6.
Reddy, J.N. and Chao, W.C., "Large-Deflection and Large-Amplitude Free Vibrations of Laminated Composite-Material Plates,"Computers and Structures , Vol. 13, p. 341 (1981).
7.
Bert, C.W. and Kumar, M., "Vibration of Cylindrical Shells of Bimodulus Composite Materials,"Journal of Sound and Vibration, Vol. 81, p. 107 (1982 ).
8.
Reddy, J.N., "Bending of Laminated Anisotropic Shells by a Shear Deformable Finite Element,"Fiber Science and Technology , Vol. 17, p. 9 (1982).
9.
Sheinman, I. and Grief, S., "Dynamic Analysis of Laminated Shells of Revolution,"Journal of Composite Materials , Vol. 18, p. 200( 1984).
10.
Noor, A.K. and Mathers, M.D., "Nonlinear Finite-Element Analysis of Laminated Composite Shells," Computational Methods in Nonlinear Mechanics J. T. Oden, E. B. Becker, R. R. Craig, R. S. Dunham, C. P. Johnson, and W. L. Oberkampf, editors, Proceedings of the International Conference on Computational Methods in Nonlinear Mechanics , Austin, Texas (1974).
11.
Reddy, J.N., "A Finite Element Analysis of Large-Deflection Bending of Laminated Anisotropic Shells,"Nonlinear Finite Element Analysis of Plates and Shells, T. J. R. Hughes, A. Pifko, and A. Jay, editors, AMD-48, ASME, p. 249( 1981).
12.
Booton, M. and Tennyson, R.C., "Buckling of Imperfect Anisotropic Circular Cylinders under Combined Loading,"AIAA Journal, Vol. 17, p. 278 (1978 ).
13.
Khot, N.S. and Bauld, N.R., Jr., "A Numerical and Experimental Investigation of Buckling Behavior of Composite Panels,"Computers and Structures , Vol. 15, p. 393(1982).
14.
Khot, N.S. and Bauld, N.R., Jr., "Further Comparison of the Numerical and Experimental Buckling Behaviors of Composite Panels,"Computers and Structures, Vol. 17, p. 61 (1983).
15.
Sheinman, I. and Simitses, G.J., "Buckling and Postbuckling of Imperfect Cylindrical Shells under Axial Compression,"Computers and Structures, Vol. 17, p. 277 (1983).
16.
Whitney, J. and Sun, C.T., "A Refined Theory for Laminated Anisotropic, Cylindrical Shells,"Journal of Applied Mechanics, ASME , Vol. 41, p. 471 (1974).
17.
Yang, T.Y., Moore, C.J. and Anderson, D.C., "Geometrically Nonlinear Formulation of a 48 D.O.F. Quadrilateral Shell Element with Rational B-Spline Geometry,"International Journal for Numerical Methods in Engineering, Vol. 21, p. 317( 1985 ).
18.
Niordson, F.I. , Introduction to Shell Theory, Solid Mechanics , Technical University of Denmark, Lyngby, Denmark (March 1980).
19.
Jones, R.M., Mechanics of Composite Materials, McGraw-Hill , New York (1975).
20.
Noor, A.K., "Hybrid Analytical Techniques for Nonlinear Analysis of Structures," Proceedings of the AIAA/ASME/ASCE/AHS 25th Structures, Structural Dynamics and Materials Conference, p. 503 (1984).
21.
Kung, L.E., Charek, L.T., Soedel, W. and Yang, T.Y., "Natural Frequencies and Mode Shapes of an Automotive Tire with Interpretation and Classification Using 3-D Computer Graphics,"Journal of Sound and Vibration, to appear (October 1985).
22.
Halpin, J.C. and Tsai, S.W., U.S. Air Force Materials Laboratory Report AFML-TR-67-423, Wright-Patterson Air Force Base, Ohio ( 1968).
23.
Riks, E., "An Incremental Approach to the Solution of Snapping and Buckling Problems,"International Journal of Solids and Structures , Vol. 7, p. 529 (1979).
24.
Wempner, G.A. , "Discrete Approximations Related to Nonlinear Theories of Solids,"International Journal of Solids and Structures, Vol. 7, p. 1581 (1971).
25.
Ramm, E., "Strategies for Tracing the Nonlinear Response Near Limit Points," in Nonlinear Elastic Analysis in Structural Mechanics, Proceedings of Europe-U.S. Workshop (ed. W. Wunderlich, E. Stein, and K.-J. Bathe), Ruhr-Universitat Bochum, Springer-Verlag (1980).
26.
Tong, P. and Pian, T.H.H., "Postbuckling Analysis of Shells of Revolution by the Finite-Element," in Thin Shell Structures, Y.C. Fung and E. E. Sechler, editors, Prentice-Hall, p. 435 (1974).
27.
Bauld, N.R., Jr. and Satyamurthy, K., "Collapse Load Analysis for Plates and Panels," AFFDL-TR-79-3038 , Air Force Wright Aeronautical Laboratories, Air Force Systems Command, Wright-Patterson Air Force Base, Ohio (1979).
