The most general axially symmetrical thermal load is one in which a transient temperature distribution, varying axially and radially, is applied to an axially symmetrical system with an irregular axial boundary. When the thermal stress equations are applied to such a system, using the conventional Gauss-Siedel or Liebmann method, severe oscillation has been experienced making convergence impossible to achieve. The authors present in this paper a method which not only converts a diverging solution but also yields a rapid rate of convergence. This method has been successfully applied to the problem of a steam turbine rotor.
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References
1.
HoyleR. D.‘Transient temperature stresses in axially symmetrical systems with special application to a solid rotor of a steam turbine’, Proc. Instn mech. Engrs1955169 (No. 31), 553.
2.
BainesB. H.HoyleR. D.‘Thermal stresses in elastic axially symmetrical bodies’, J. mech. Engng Sci.19624 (No. 2), 111.
3.
FrankelS. P.‘Convergence rate of iterative treatments of partial difference equations’, Mathematical tables and other aids to computation19504 (Nos 29–32).
4.
ChowC. L.Computation of transient temperatures and stresses in steam turbine rotors1965 Thesis presented to the University of London for the degree of Ph.D.
RichardsonL. F.‘The approximate arithmetical solution by finite differences of physical problems involving difference equations with an application to the stress in a Mansory dam’, Phil. Trans. R. Soc.1911210, 307.
7.
TempleG.‘Relaxation methods applied to linear systems’, Proc. R. Soc.1939169 (Series A), 476.
8.
TrumplerW. E.jun. ‘The creep phenomenon as it affects steam turbine rotors’, A.S.M.E. paper No. 42, 1963, 69.
9.
BerryW. R.JohnssonI.‘Prevention of cyclic thermal-stress cracking in steam turbine rotors’, A.S.M.E. paper No. 63-PWR-16, 1963.
10.
JacksonR. L.CoulterS. B.‘Operation of steam turbine to minimize shell cracking’, Trans. Am. Soc. mech. Engrs, Engng for Power1960 (July), 227.
