Flamant problem of a cubic quasicrystal half-plane

The Flamant problem of a cubic quasicrystal half-plane is solved when its surface is loaded by normal and tangential concentrated forces. Its solution serves as a fundamental solution since its superposition forms other solutions. The Flamant problem is converted to an associated boundary value problem. The Fourier transform method is applied to solve the Flamant problem. Explicit expressions for the fundamental solution of the phonon and phason stresses are obtained. A comparison between the fundamental solutions of the Flamant problem for cubic quasicrystals and conventional cubic crystals is made. The influence of the presence of phason field on the phonon stress and deformation is shown in graph.

Automated summary

The Flamant problem of a cubic quasicrystal half-plane under normal and tangential concentrated forces has been solved. This solution serves as a fundamental solution for other problems. The Fourier transform method is applied to obtain explicit expressions for the fundamental solution of the phonon and phason stresses. A comparison between the fundamental solutions of cubic quasicrystals and conventional cubic crystals is made, illustrating the influence of the phason field on the phonon stress and deformation.