THREE-DIMENSIONAL GENERAL SOLUTION OF TRANSVERSELY ISOTROPIC THERMOELASTICITY AND THE POTENTIAL THEORY METHOD
横观各向同性三维热弹性力学通解及其势理论法

By the introduction of two displacement functions, the equations of motion in terms of displacement for a transversely isotropic elastic medium with thermal effect are simplified. The general solution of dynamic problem for the uncoupled thermoelastic theory is strictly derived utilizing the operator theory. It can be expressed by two functions: one satisfies a second-order wave equation and the other satisfies a sixth-order homogeneous partial differential equation. For static problem, the general solution is further simplified by virtue of the generalized Almansi's theorem, and can be expressed in terms of four quasi-harmonic functions. The problem of a flat crack located in a plane perpendicular to the symmetric axis and distributed with prescribed temperature is investigated. The potential theory method proposed by Fabrikant is generalized for thermoe-lasticity. A new potential corresponding to the temperature field is introduced, and consequently, an integral equation and an integro-differential equation are derived. For a penny-shaped crack with uniform distributing temperature, exact solutions can be obtained using Fabrikant's results. It is found that all expressions for the thermoelastic field can be expressed in terms of elementary functions. The stress intensity factor at the crack tip is derived exactly. Comparison with existent results shows a good agreement. Moreover, the proposed method can be used to analyze non-axisymmetric problems such as a penny-shaped crack subjected to a point temperature load, for which the Hankel transform method can not be utilized. Further results in this respect will be reported in other papers.