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Acta Mechanica

, Volume 7, Issue 4, pp 299–310 | Cite as

Influence lines for bending under a ring load of a free shell, a shell embedded in a soft medium and a shell containing a soft core

  • C. V. Yogananda
Contributed Papers

Summary

Theoretical expressions for stresses and displacements have been derived for bending under a ring load of a free shell, a shell embedded in a soft medium, and a shell containing a soft core. Numerical work has been done for typical cases with anElliot 803 Digital Computer and influence lines are drawn therefrom.

Keywords

Dynamical System Fluid Dynamics Transport Phenomenon Typical Case Digital Computer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

A (α),B (α)

Functions of α

a, t

Mean radius and thickness of the shell

ES,μS

Young's modulus andPoisson's ratio of the shell

Gc,μc

Shear modulus andPoisson's ratio of the casting or core

I0r),I1r)

ModifiedBessel functions of the first kind and order zero and one respectively

K0r),K1r)

ModifiedBessel functions of the second kind and order zero and one respectively

p

Ring load, lb/in

U, W

Displacement components in the casing or core in thez andr direction

u, w

Displacement components of a middle surface point in the shell

σr,τrz

Radial and shearing stress components

α

Independent variable of infinite integrals

k

[3(1–μS2)a2/t2]1/4

Einflußlinien für die Biegung einer freien Schale, einer Schale in einer weichen Bettung und einer Schale mit weichem Kern

Zusammenfassung

Für die Biegung einer freien Schale, einer weich gebetteten Schale und einer Schale mit weichem Kern unter einer Ringlast werden Ausdrücke für die Spannungen und Verschiebungen hergeleitet. Die Ergebnisse wurden für einige typische Fälle mit einem DigitalrechnerElliot 803 numerisch ausgewertet. Die sich ergebenden Einflußlinien wurden graphisch dargestellt.

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References

  1. [1]
    Klosner, J. M. andJ. Kempner: On a comparison of elasticity and shell theory solutions. Pibal Report No. 493. Polytechnic Institute of Brooklyn. May 1959.Google Scholar
  2. [2]
    Karman, Th. V. andM. A. Biot: Mathematical methods in Engineering. McGraw Hill Book Co., New York. 1940. 343–347.Google Scholar
  3. [3]
    Yogananda, C. V.: On a unified elasticity and shell theory solution for a cylindrical shell enclosed in an elastic casing. Int. J. Engg. Sci (USA),5, 681–688, 1967.Google Scholar
  4. [4]
    Yogananda, C. V.: Ring loading of a long, thin circular cylindrical shell enclosing a soft, solid core—a recalculation by the Love function method of elasticity. Int. J. Mech. Sci. (England),8, 751–757 (1966).Google Scholar

Copyright information

© Springer-Verlag 1969

Authors and Affiliations

  • C. V. Yogananda
    • 1
  1. 1.Department of Mechanical EngineeringIndian Institute of ScienceBangalore-12India

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