The plane problem of two-dimensional decagonal quasicrystals with a rigid circular arc inclusion was investigated under infinite tension and concentrated force. Based on complex representations of stresses and displacements of two-dimensional decagonal quasicrystals, the above problem is transformed into Riemann boundary problem by using the analytic continuation principle of complex functions. The general solutions of two-dimensional decagonal quasicrystals under the action of plane concentrated force and infinite uniform tension are derived. The closed solutions of complex potential functions in several typical cases are obtained, and the formula of singular stress field at the tip of rigid line inclusions is given. The results show that the stress field at the tip of circular arc rigid line inclusions has singularity of oscillation under plane load. Numerical examples are given to analyze the effects of inclusion radius, different inclusions, the coupling coefficient and phason field parameter on stress singularity coefficients.

In this paper, the thermal mechanical coupling problem of an infinite two-dimensional decagonal quasicrystal matrix containing elastic elliptic inclusion is studied under remote uniform loading and linear temperature variation. Combining with the theory of the sectional holomorphic function, conformal transformation, singularity analysis, Cauchy-type integral and Riemann boundary value problem, the analytic relations among the sectional functions are obtained, and the problem is transformed into a basic complex potential function equation. The closed form solutions of the temperature field and thermo-elastic field in the matrix and inclusion are obtained. The solutions demonstrate that the uniform temperature and remote uniform stresses will induce an internal uniform stress field. Numerical examples show the effects of the thermal conductivity coefficient ratio, the heat flow direction angle and the elastic modulus on the interface stresses. The results provide a valuable reference for the design and application of reinforced quasicrystal materials.