十二次对称二维准晶中的无摩擦接触问题

利用积分变换的方法讨论了在一个刚性压头作用下十二次对称二维准晶的无摩擦接触问题. 通过引入位移势函数，将数量巨大而复杂的偏微分方程转化为两个独立的双调和方程，应用Fourier分析与对偶积分方程理论解决了十二次对称二维准晶材料的无摩擦接触问题，得到了相应的接触应力解析表达式，结果表明：如果接触位移是一常数，则接触应力在接触区域边缘具有-1/2阶奇异性；反之，如果接触应力在接触区域边缘具有-1/2阶的奇异性，则接触位移一定为一常数，这为准晶材料的接触变形提供了重要的力学参数.

Frictionless Contact Problem of Dodecagonal System in Two-dimensional Quasicrystals

Frictionless contact problem of dodecagonal system in two-dimensional quasicrystals is researched by using integral transform method. By introducing displacement functions, the complicated partial differential equations of the plane elastic problems of dodecagonal system in two-dimensional quasicrystals are turned into two independent biharmonic equations. A contact problem with action of a rigid flat die in the dodecagonal system in two-dimensional quasicrystalline material was solved by using Fourier analysis and dual integral equations theory. The results show that if the contact displacement is a constant in the contact zone, the vertical contact stress has -1/2order singularity in the edge of the contact zone, which provide the important mechanics parameter for contact deformation of quasicrystalline material.