This paper is concerned with an axisymmetric transient thermoelastic problem for a transversely anisotropic hollow cylinder, the boundary of internal surface being subjected to a sudden temperature rise. The problem is treated on assumption that the thermal and elastic properties of the cylinder are dependent on temperature. Basic equation is solved with the aid of perturbation method. The particular boundary value problems are carried out, and the corresponding displacements and stresses are clarified. For numerical examples, calculations are performed for the cases of anisotropic cylinders made of grades ATJ and ZTA graphites respectively. In these treatments, the variation of conductivity and thermal expansion is taken to be linear according to the temperature rise, but that of the Young's moduli is taken to be quadratic. The solution for an isotropic cylinder is also derived as a particular case of the present problem.

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It is demonstrated by a simple example and an elementary calculation that under certain conditions the moment of a dipole fitted to a distribution of magnetic potential is not necessarily the same as the dipole moment in the original magnetic potential. The dipole moment of the original magnetic potential which is a vector quantity specified by the first three coefficients in the spherical harmonic expansion is invariant, that is, independent of the choice of the origin of the coordinate system. Despite this, the moment of the fitted dipole can be different from the dipole moment in the original magnetic potential, depending on the choice of the optimum condition for the fitting. The optimum condition used here differs from that adopted in Schmidt's definition in that in the present definition coefficients of all degree and order are considered. The present definition becomes identical with Schmidt's definition when the harmonics of degrees higher than the quadrupole are truncated. When all the higher harmonics are included in the definition, we obtain a moment and location of the dipole different from those obtained from the classical method of Schmidt. Moreover, the obtained dipole moment and location are different from those deduced from a generalization of Schmidt's definition by inclusion of all harmonics to the infinite degree. For the present geomagnetic field, this method of analysis gives a dipole position shifted from the conventional eccentric dipole position roughly by 80km, and a moment reduced roughly by 20nT.

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Elasto-plastic constitutive equations which take into account yield-vertex effects are important in the study of localization instabilities of plastic deformations. However, they have never been discussed thermomechanically. In this paper, a method of deriving the above equations is proposed which is based on the second law of thermodynamics and the principle of maximal entropy production rate. Elastic strain as a strain measure which is conjugate to the objective stress rate is separated from total strain so that the Clausius-Duhem inequality, in which the Gibbs function is introduced as an elastic potential, can be always satisfied. The strain rate and stress rate are expressed by the same objective rate in the rate form of the elastic constitutive equation obtained. The plastic constitutive equation is derived using the principle of maximal dissipation rate. Since this equation is regarded as a flow rule in which the complementary dissipation function assumes the role of a plastic potential, it is indicated that the yield-vertex can exist on the dissipation surface. Furthermore, the spin which should be used in the objective stress rate is selected by taking into account not only usual requirements but also thermomechanical ones.

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