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Elastic limits of a radially heated thick-walled cylindrically curved panel

Elastische Grenzlasten eines radial erhitzten dickwandigen zylindrisch gekrümmten Paneels

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Abstract

In analogy to the theory of wide curved beams, the basic equations for a cylindrically curved panel of homogeneous thickness in a state of plane strain subject to a radial temperature gradient are derived. The ends of this thick-walled shell are presupposed to be guided in such a way that a displacement in circumferential direction may occur and that the radius of the initial middle surface remains unchanged. Then, couples act on those ends, giving rise to pure bending conditions. Based thereon, the stresses occurring for a heated inner and/or outer surface are analyzed, and—taking thermal softening and hence a reduced yield stress into account—the elastic limits according to the yield criteria of Tresca and von Mises are discussed comprehensively.

Zusammenfassung

In Analogie zur Theorie dicker gekrümmter Stäbe werden die Grundgleichungen für ein zylindrisch gekrümmtes Paneel von homogener Dicke unter ebener Verzerrung bei Auftreten eines radialen Temperaturgradienten angegeben. Es wird vorausgesetzt, daß die Lagerung der dickwandigen Schale eine Verschiebung in Umfangsrichtung zulässt und daß der Radius der ursprünglichen Mittelfläche sich nicht ändert. Die dann an diesen Seiten auftretenden entgegengesetzt gleichen Momente bewirken einen Zustand reiner Biegung. Die dadurch entstehenden Spannungen werden für den Fall einer erhitzten Innen- und/oder Außenfläche des Paneels untersucht, und es werden – unter Berücksichtigung einer mit wachsender Temperatur abnehmenden Fließspannung – die elastischen Grenzlasten sowohl für das Trescasche als auch das von Misessche Fließkriterium umfassend diskutiert.

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Abbreviations

a :

inner surface radius of the panel

b :

outer surface radius of the panel

C i :

constants of integration

E :

modulus of elasticity

f :

function of θ

L i :

auxiliary expressions

M :

couple (per unit length in axial direction)

r :

radius

r 0 :

radius of the (initial) middle surface

T :

difference of absolute and reference temperature

T a :

temperature of the inner surface

T b :

temperature of the outer surface

u :

displacement in radial direction

v :

displacement in circumferential direction

:

non-dimensional quantity

α :

coefficient of thermal expansion

β :

thermal softening parameter

γ rθ :

shear strain

ΔT :

temperature difference (T b −T a )

ϵ r ,ϵ θ ,ϵ z :

normal strain components

ν :

Poisson’s ratio

σ eM :

equivalent stress according to von Mises

σ eT :

equivalent stress according to Tresca

σ r ,σ θ ,σ z :

normal stress components

σ th :

yield stress at temperature T

σ 0 :

uniaxial yield limit at reference temperature

τ rθ :

shear stress

ϕ :

constant of integration

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Acknowledgements

E. Arslan gratefully acknowledges the financial support of Vienna University of Technology and Inonu University during the performance of parts of this investigation in Vienna.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Inonu University, 44280, Malatya, Turkey

    E. Arslan

  2. Institute of Mechanics and Mechatronics, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040, Vienna, Austria

    W. Mack & U. Gamer

Authors
  1. E. Arslan
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  2. W. Mack
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  3. U. Gamer
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Correspondence to W. Mack.

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Arslan, E., Mack, W. & Gamer, U. Elastic limits of a radially heated thick-walled cylindrically curved panel. Forsch Ingenieurwes 77, 13–23 (2013). https://doi.org/10.1007/s10010-013-0162-6

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  • DOI: https://doi.org/10.1007/s10010-013-0162-6

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