In the present article, we deal with spherically symmetric isothermal and thermo elastic problems of a transversely isotropic, inhomogeneous hollow sphere, analytically. We assume that material properties such as the thermal conductivities, the Young's moduli and the coefficients of linear thermal expansion are independently varied in a form of power with radial coordinate γ, and that they also have same properties in θ-φ plane whereas those in the radial direction differ from those in θ-φ plane. We formulate the equation of heat conduction in a steady state and the displacement equation of equilibrium for the hollow sphere under spherically symmetric condition. Thereafter we derive analytical solutions of displacement and stress components for the hollow sphere which is subject to uniform pressures or uniform heat supply at inner and outer boundary surfaces. We carry out numerical calculation and discuss the effect of interaction between material anisotropy and material inhomogeneity on the mechanical behavior of the hollow sphere.
In this paper, making use of the strain increment theorem, the transient thermoelastoplastic bending problem of an infinite plate is discussed. In order to develop the analysis for the temperature field, the methods of Fourier cosine and Laplace transforms are introduced, and the theoretical solution is obtained. On the other hand, for the development of the thermoelastoplastic field, both the analytical technique of Airy's stress function method for thermoelastic behavior and the numerical technique of the finite difference method for the plastic behavior are applied. However, difficulty in applying the finite difference method may occur. It is clearly impossible to cover an infinite region with a finite difference grid. Thus we have introduced the assumption that plastic deformation is restricted to a local region. Thereafter, based on Dixon's experimental results that the stress field outside the plastic region is the same as the elastic stress field, namely, the elastic solution prevails outside the plastic region, the finite difference method is applied to the finite region predicted to show the plastic deformation. Some numerical results, such as the plastic deformation in the out-of-plane direction, are shown in figures and discussed briefly.
Thermal stresses are repeatedly applied to members due to temperature cycle of heating and cooling. Then, the members often fail due to the repeated stresses as a result of inelastic behaviors and fatigue deformations. This study is concerned with a plane axisymmetrical transient thermal stress problem of a hollow circular cylinder under a cyclic heating. Analytical solutions of temperature change, displacement and stress components in the cylinder are derived. Furthermore, numerical calculations are performed under the condition that inner surface of the cylinder is exposed to a sinusoidally varying temperature, outer one is kept at typical temperature. Repeats of tension and compression in thermal stresses are applied to the cylinder, which are resulted from the temperature cycle. In particular, it's found that normal stresses in circumferential and axial directions of the cylinder are much larger.
In the present study, dynamic and quasi-static behaviors of magneto-thermo-elastic stresses and deformations in a conducting infinite plate subjected to an arbitrary variation of magnetic field are investigated. It is assumed that a time-varying magnetic field which is defined by an arbitrary function of time acts on both side surfaces of the infinite plate in the direction parallel to its surfaces. Fundamental equations of one-dimensional electromagnetic, temperature and elastic fields are formulated. Then, solutions of magnetic field, eddy current, temperature change and both dynamic and quasi-static solutions of stresses and deformations are analytically derived. The solutions of stresses are determined to be sums of thermal stress caused by eddy current loss and magnetic stress caused by Lorentz force. The dynamic and quasi-static behaviors of the stresses are examined by numerical calculations.
