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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 .
As a new kind of solid matter structure, quasicrystals bring profound changes to the traditional condensed matter physics, and its elastic basic equations are much more complex than the traditional elastic fundamental equations.During the introduction of the displacement function and the application of Fourier analysis and duality The integral equation theory satisfactorily solves the contact problem of ten times two-dimensional quasicrystal material under the action of a flat-bottomed punch, and obtains the analytic expression of the stress and displacement of the material contact problem.The results show that if the contact displacement is one in the contact area Constant, the vertical contact stress has a - ½ step singularity at the contact edge, which provides an important amount of mechanics for the contact deformation of the quasicrystalline material.