This paper treats some problems in a homogeneous transversely isotropic elastic material, occupying an infinite space, or an infinitely long circular cylinder. The analysis is based upon the potential function method by Elliott, with the addition of another potential function. The static solution is extended to include quasi-static, or steady-state problems. Closed-form solution is found for the problem of an arbitrarily oriented concentrated force in an infinite medium. The case of discontinuous pressure over an infinitely long circular cylinder is also studied with the aid of a numerical method of integration. The applied forces are assumed to be moving with uniform velocity along the anisotropic direction.

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