A first approximation theory for the unsymmetric deformation of non- homogeneous, anisotropic, elastic cylindrical shells is derived by means of the asymptotic integration of the elasticity equations. For a homogeneous, isotropic material, the equations reduce to the Donnell equations. The appli cation to a cylinder under combined loading is shown.
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References
1.
S. W. Tsai, J. C. Halpin and J. M. Whitney, Editors, Composite Materials Workshop, Technomic Publishing Co., Inc., Westport, Conn., (1968 ).
2.
G. Herrmann, Editor, Dynamics of Structured Solids, American Society of Mechanical Engineers, New York, (1968).
3.
A.L. Goldenveizer , "Methods for Justifying and Refining the Theory of Shells," P.M.M., Vol. 32 (1968), p. 684.
4.
W.T. Koiter, "Foundations and Basic Equations of Shell Theory. A Survey of Recent Progress," in Theory of Thin Shells, F. I. Niordson, Editor, Springer-Verlag, Berlin/ Heidelberg, ( 1970), p. 93.
5.
S. A. Ambartsumian, Theory of Anisotropic Shells, NASA TT F-118, (1964).
6.
G. Pickett and M.W. Johnson, Analytical Procedures for Predicting the Mechanical Properties of Fiber Reinforced Composites, Part II, Air Force Materials Laboratory TR-65-220, (1966).
7.
M.W. Johnson and O.E. Widera, On the Dynamic Theory of Non-Homogeneous Plates, Materials Engineering Department TR-69-2, University of Illinois at Chicago Circle , (1969).
8.
L.H. Donnell, Stability of Thin-Walled Tubes Under Torsion, NACA TR-479, ( 1933).
9.
M.W. Johnson , "A Boundary Layer Theory for the Unsymmetric Deformations of Circular Cylindrical Elastic Shells," J. Math. Phys., Vol. 42 (1963), p. 167.
10.
M.W. Johnson and O.E. Widera, "An Asymptotic Dynamic Theory for Cylindrical Shells," Studies in Appl. Math., Vol. 48 (1969), p. 205.
11.
O.E. Widera , "Asymptotic Theories for the Unsymmetric Vibrations of Cylindrical Shells, Part I: Derivation - Part II: Application," J. Appl. Math. Phys. (ZAMP), Vol. 21 ( 1970), p. 378.
12.
M.W. Johnson and E. Reissner, "On the Foundations of the Theory of Thin Elastic Shells," J. Math. Phys., Vol. 37 (1959), p. 371.
13.
C.W. Bert, "Structural Theory for Laminated Anisotropic Elastic Shells," J. Composite Materials, Vol. 1 ( 1967), p. 414.
14.
C.W. Bert, J.L. Baker and D.M. Egle, "Free Vibrations of Multilayer Anisotropic Cylindrical Shells," J. Composite Materials, Vol. 3 ( 1969), p. 480.
15.
J.M. Whitney and J.C. Halpin, "Analysis of Laminated Anisotropic Tubes Under Combined Loading," J. Composite Materials, Vol. 2 (1968), p. 360.
16.
N.J. Pagano and J.M. Whitney, "Geometric Design of Composite Cylindrical Shell Characterization Specimens," J. Composite Materials, Vol. 4 (1970), p. 360.
17.
R.R. Rizzo and A.A. Vacario, "A Finite Element Analysis of Laminated Anisotropic Tubes," J. Composite Materials, Vol. 4 (1970), p. 344.
