O pewnym quasi-ustalonym zagadnieniu termosprężystości

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 (σ_ij) 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 (σ_ij). These components do not, however, satisfy all boundary conditions, the stresses σ_xz and σ_yz not vanishing in the plane z = 0. The state (σ_ij) satisfying the boundary conditions (1.21) in the plane z = 0, should be superposed over the stresses (σ_ij). The (σ_ij) components are determined by means of the displacement function of B.G. Ga1erkin. The superposition of the stresses (σ_ij) and (σ_ij) gives the stress (σ_ij), 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.