O pewnym quasi-ustalonym zagadnieniu termosprężystości - NOWACKI, Witold (Engineering Transactions, 1957)
A quasi-steady state three-dimensional thermo-elastic problem The object here is to determine the state of stress in an elastic semi-space due to the action of a source of heat of intensity W, moving with a constant velocity v in the plane bounding the semi-space. Allowing a heat dipole to act in the plane z = 0, a temperature field is obtained, (1.14) and (1.15), satisfying the boundary conditions (T = 0) in the plane z = 0, and at infinity. The stress components (σij) are determined by means of the thermo-elastic potential of displacements Φ satisfying the equation (1.6). The knowledge of a particular integral of this equation the Eqs. (1.16) and (1.17) enables us to determine, on the basis of the Eqs. (1.11), the stress components (σij). These components do not, however, satisfy all boundary conditions, the stresses σxz and σyz not vanishing in the plane z = 0. The state (σij) satisfying the boundary conditions (1.21) in the plane z = 0, should be superposed over the stresses (σij). The (σij) components are determined by means of the displacement function of B.G. Ga1erkin. The superposition of the stresses (σij) and (σij) gives the stress (σij), which is sought. Finally, consideration is given to the particular case of the state of stress due to a linear heat source uniformly distributed along the z-axis and moving in the x-direction with a constant velocity.