中文摘要：

准晶作为一种新的固态物质结构给传统的凝聚态物理学带来了深刻的变革，其弹性基本方程比传统晶体的弹性基本方程要复杂得多.通过引入位移函数和应用Fourier分析与对偶积分方程理论圆满解决了在一个平底冲头作用下十次二维准晶材料的接触问题，得到了此材料接触问题应力与位移的解析表达式.结果表明，如果接触位移在接触区域内为一常数，则垂直接触应力在接触边缘具有-1/2阶奇异性，这为准晶材料的接触变形提供了重要的力学量.

英文摘要：

As a new structure of solid matter quasicrystal brings profound new ideas to the traditional condensed matter physics, its elastic equations are more complicated than that of traditional crystal. A contact problem of decagonal two? dimensional quasicrystal material under the action of a rigid flat die is solved satisfactorily by introducing displacement function and using Fourier analysis and dual integral equations theory, and the analytical expressions of stress and displacement fields of the contact problem are achieved. The results show that if the contact displacement is a constant in the contact zone, the vertical contact stress has order -1/2 singularity on the edge of contact zone, which provides the important mechanics parameter for contact deformation of the quasicrystal.