O pewnym ustalonym zagadnieniu przestrzennym termosprężystości - NOWACKI, Witold (Engineering Transactions, 1957)
A steady-state three-dimensional thermo-elastic problem The object of this paper is to determine the temperature field T and the stress components (σij) in an elastic semi-space, assuming that the temperature in the region Γ of the plane bounding the semi-space is known and equal to T0(ξ, η), the region outside Γ being kept at T = 0. The problem is solved by means of the Green’s function. The temperature field T* is determined and the stress components (σij*), in the case where T = 0 over the whole plane z = 0 except an infinitely small region dΓ where T = T0. Using integral expressions (1.1) and (1.2), T and σij are determined for any temperature distribution T0(ξ, η) inside the region Γ. In the second part of the paper, the Green’s functions T* and Φ* and the Galerkin’s function φ are determined, using the Fourier transformation. The Green’s functions obtained for the stress (σij*) are characterized by the fact that the three components σzz*, σzx*, and σzy* are zero. In the third part of the paper, consideration is given to the particular case of T0 = const over a rectangle whose sides are 2a and 2b, and that of T0 = const over an infinite strip of width 2a. In the latter case, only the stress σyy* differs from zero.