A steady line heat source in a decagonal quasicrystalline half-space

The problem of a steady line heat source within a decagonal quasicrystalline half-space, in which the boundary is traction-free, is investigated in detail by applying the complex variable technique. The line heat source is infinitely long in the period direction, then the plane strain condition prevails. The four complex stress functions are derived. It is found that the determination of the complex stress functions is independent of the thermal boundary conditions. The stress fields induced by the heat source are explicitly given based on the complex stress functions. Furthermore, we consider, both qualitatively and quantitatively, the distribution of σ₁₁ on the boundary y = 0 of the half-space to demonstrate the influence of the phonon–phason coupling constant R on the stress field.