Three-dimensional thermo-elastic general solutions of one-dimensional hexagonal quasi-crystal and fundamental solutions

This Letter presents three-dimensional general solutions for static problems in thermo-elasticity of one-dimensional hexagonal quasi-crystals. Two displacement potentials are introduced to simplify the equilibrium equations in terms of displacement and temperature. Rigorous operator theory and generalized Almansiʼs theorem are applied to derive the general solutions in terms of five quasi-harmonic functions. To show the significance of the general solutions, a semi-infinite space and an infinite space, both of which are subjected to a heat source, are considered. In these two cases, closed form fundamental phonon–phason-elastic fields are expressed by elementary functions, which play an important role in numerical simulations. ► We present 3D static thermo-elastic general solutions for 1D hexagonal QCs. ► Thermo-phonon–phason field is expressed by five quasi-harmonic functions. ► Fundamental solutions for semi-infinite and infinite spaces are derived.