中文摘要：

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．

英文摘要：

Quasicrystal, a new kind of solid material, exhibits high hardness and abrasion resistance. It has been widely used in engineering as coating on bearing or other machinery parts to reduce stress concentration and surface abrasion. Therefore, the contact mechanics of quasicrystal has become a very useful research topic. In order to obtain the mechanical indentation responses of quasicrystal, and to understand the mechanical and physical properties of quasicrystal more comprehensively, this study was aimed at in- vestigating the frictionless contact problem of dodecagonal system in two-dimensional quasicrystal based on its low friction properties. A frictionless contact problem of dodecagonal system in two-dimensional quasicrystal was solved by introducing the displacement potential function and using the integral transform method and dual integral equation theory. The complicated partial differential equations of the plane elastic problem of dodecagonal system in two-dimensional quasicrystal were transformed into two independent biharmonic equations, which together with all field varieties, were transformed into Fourier integral expressions. Through a combination of these Fourier integral expressions and boundary conditions of the contact problem, two independent dual integral equations were obtained. Finally, the contact stress and displace- ment of the dodecagonal system in two-dimensional quasicrystal material under the rigid flat indenter were achieved by solving the dual integral equations. The numerical results showed that if the contact displace- ment was a constant in the contact zone, the vertical contact stress had a --1/2 order singularity at the edge of the contact zone, which could provide important mechanical parameters for the contact deformation of quasicrystal material. The results also proved that classical elastic theory was suitable for quasicrystal contact analysis, which supplied a theoretical basis for expanding its application.