Advertisement

Acta Mechanica

, Volume 8, Issue 1–2, pp 82–103 | Cite as

Large deflections of heated circular plates

  • M. C. Pal
Contributed Papers

Summary

Large deflections of heated circular plates with or without a concentric circular hole and with different boundary conditions and temperature distributions are analyzed in the light ofBerger's analysis. The subject is treated in a simple and unified manner. Numerical results are shown in graphical form.

Keywords

Boundary Condition Dynamical System Temperature Distribution Fluid Dynamics Transport Phenomenon 
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

d, a, b

Thickness, outer and inner radius of the plate, respectively

p

Aerodynamic pressure normal to the plate

u, v, w

Displacement components in the median surface in ther, θ andz directions, respectively

D

Flexural rigidity

E

Modulus of elasticity

T

Temperature rise above the unstrained state

Π

Total potential energy

α

Coefficient of thermal expansion

ε11,ε22

Extensional strains in ther and θ directions, respectively

ε12

Shearing strain in ther θ-plane

σ11,σ22

Extensional stresses in ther and θ directions, respectively

ν

Poisson ratio\(\begin{gathered} \nabla ^2 = \frac{{d^2 }}{{dr^2 }} + \frac{1}{r}\frac{d}{{dr}}. \hfill \\ \varsigma = \frac{b}{a}. \hfill \\ \end{gathered} \)

Große Durchbiegungen geheizter Kreisplatten

Zusammenfassung

Große Durchbiegungen geheizter Kreisplatten und Kreisringplatten werden bei verschiedenen Randbedingungen und Temperaturfeldern im Licht derBergerschen Analyse untersucht. Der Gegenstand wird in einfacher und vereinheitlichter Weise behandelt. Numerische Ergebnisse werden in graphischer Form gebracht.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Sunakawa, M.: Thermal deformation of a circular plate, Aeron. Res. Inst., Univ. of Tokyo, Bulletin2 (1961), 269.Google Scholar
  2. [2]
    Berger, H. M.: A new approach to the analysis of large deflections of plates. J. Appl. Mech.22 (1955), 465.Google Scholar
  3. [3]
    Boley andWeiner: Theory of Thermal Stresses. John Wiley and Sons, Inc. 1960.Google Scholar
  4. [4]
    Timoshenko, S. andW. S. Krieger: Theory of Plates and Shells. McGraw-Hill, Inc. 1959.Google Scholar
  5. [5]
    Nash, W. A. andJ. R. Modeer: Certain approximate analysis of non-linear behavior of plates and shallow shells. Proc. Symp. on the Theory of Thin Elastic Shells, Delft, The Netherlands, August, 1959.Google Scholar
  6. [6]
    Thein Wah: Vibration of circular plates at large amplitudes, Proc. ASCE, J. Engg. Mech. Div. EM5, pp. 1–15 (Oct. 1963).Google Scholar
  7. [7]
    Sinha, S. N.: Large deflections of plates on elastic foundation. Proc. ASCE. J. Engg. Mech. Div. EM1, pp. 1–24 (Feb. 1963).Google Scholar
  8. [8]
    Basuli, S.: Note on the large deflection of a circular plate under a concentrated load. Z. angew. Math. Mech.12, (1961) 357.Google Scholar
  9. [9]
    Carslaw, H. S. andJ. C. Jaeger: Conduction of Heat in Solids. Oxford Univ. Press. 1959.Google Scholar
  10. [10]
    Gajendar, N.: Large amplitude vibrations of plates on elastic foundations. Int. J. Non-linear Mech. Vol.2, pp. 163–172.Google Scholar
  11. [11]
    Poincaré, H.: Les Méthodes de la Mécanique céleste. Paris,1, (1892) 32.Google Scholar
  12. [12]
    Gatewood, B. E.: Thermal Stresses. McGraw-Hill, 1957.Google Scholar

Copyright information

© Springer-Verlag 1969

Authors and Affiliations

  • M. C. Pal
    • 1
  1. 1.Department of MathematicsIndian Institute of TechnologyKharagpurIndia

Personalised recommendations