Naprężenia Cieplne w Powłoce Kulistej oraz Cylindrycznej w Przypadku Materiałów o Własnościach Zależnych Od Temperatury

A one-dimensional steady-state thermoelastic problem is considered, consisting in determining the stresses in a thick-walled cylindrical and spherical shell if the inner and outer surface are heated to different temperatures T0 and T1. It is assumed in addition that the elastic (E) and thermal properties (λ, a) of the material vary with the temperature in an arbitrary manner. With these assumptions general equations for stresses are derived in Sec. 2 and 4 for plane stress and strain and in the case of the spherically symmetric thermo-elastic problem (the problem of the hollow Ephere). This is done on the basis of the displacement equations obtained in Sec. 2 and the solutions of the non-linear heat equations derived in Sec. 3. A discussion of these equations, in Sec. 4, gives a certain idea of the degree in which the variability of the coefficient of heat conduction, λ = λ(T), influences the form and the extremum values of the stresses. 'In the case of certain heat resisting materials, and with considerable temperature differences (T1–T0) this influence may prove to be relatively high and amounts to ten or twenty per cent of the maximum stress, or even more.