Plates and Shells

Course Description:

This course covers the mechanics of plates using classical theory (cylindrical bending, rectangular plates, and circular plates) and plate theory with shear deformation. Includes combined effects of bending and in-plane forces, buckling of plates, moderately large deflections, membrane theory of shells, analysis of thin cylindrical shells of revolution, and general theory of thin elastic shells.

Textbook:

Thin Plates and Shells: Theory, Analysis and Applications by Eduard Ventsel and Theodor Krauthammer Marcel Dekker, Inc. New York, Basel, ISBN: 0-8247-0575-0
and lecture notes.

Topics Covered:
  1. Introduction
    THIN ELASTIC PLATES
  2. Governing Equations of Small Deflection Plate Theory
  3. Analytical Solutions for Rectangular Plates
  4. Analytical Solutions for Circular Plates
  5. Large Deflection Theory of Plates
  6. Advanced Topics (As time allows)
    - Multilayered plates
    - Sandwich plates
    - Buckling of plates
    - Vibration of Plates
    THIN ELASTIC SHELLS
  7. Introduction
  8. Geometry of the middle surface
  9. General Theory of Shells
  10. Membrane theory of shells
  11. Bending Theory of Shells
References
  • Theory of Plates and Shells, S.P. Timoshenko and S. Woinkowsky-Krieger, McGraw-Hill Book Company, NY. 2nd edition 1959, reissued 1987 (QA931 .T56 1959)
  • Stresses in Shells. W. Flügge, Springer-Verlag, Berlin, 2nd Edition, 1960, 2nd printing, 1990 (TA660.S5 F58 1973).
  • Beams, Plates and Shells, L.H. Donnell, McGraw-Hill Book Company, NY., 1976 (TA660.B4 D66)
  • Shell Theory, F. I. Niordson, North-Holland, Amsterdam, 1985 (TA660.S5 N56 1985)
  • Stresses in Plates and Shells, A. Ugural, McGraw Hill, 1999. ( TA660.P6 U39 1999)
  • Analysis of Shells and Plates, P.L. Gould, Springer-Verlag, 1988, (TA660.S5 G644 1988)
  • Structural mechanics: the behavior of plates and shells, J. R. Vinson, Wiley, New York, 1974, ( TA660.P6 V55 1974)
  • The Buckling of Plates and Shells, H.L. Cox, Macmillan, NY, 1962 (TA460 .C6x)
  • Introduction to the Theory of Shells, C.L. Dym, Hempshire Publishing Corp., 1990. (QA935 .D89 1990)
  • The Behavior of Thin Walled Structures: Beams, Plates and Shells, J.R. Vinson, Dordrecht, Netherlands ; Boston : Kluwer Academic Publishers, 1989 (TA660.T5 V56 1989).
  • Theory of Elastic Stability, S.P. Timoshenko and J.M. Gere, McGraw-Hill, NY, 1961, (QA931 .T54 1961)