## 留言板

 引用本文: 赵雪芬, 李星. 带裂纹十次对称二维准晶平面弹性的无摩擦接触问题[J]. 应用数学和力学, 2019, 40(2): 223-236.
ZHANO Xuefen, LI Xing. A Frictionless Contact Problem of 2D Decagonal Quasicrystal Plane Elasticity With Cracks[J]. Applied Mathematics and Mechanics, 2019, 40(2): 223-236. doi: 10.21656/1000-0887.390127
 Citation: ZHANO Xuefen, LI Xing. A Frictionless Contact Problem of 2D Decagonal Quasicrystal Plane Elasticity With Cracks[J]. Applied Mathematics and Mechanics, 2019, 40(2): 223-236.

• 中图分类号: O343

## A Frictionless Contact Problem of 2D Decagonal Quasicrystal Plane Elasticity With Cracks

Funds: The National Natural Science Foundation of China(11762017)
• 摘要: 借助经典平面弹性复变函数方法，研究了单个刚性凸基底压头作用下，带任意形状裂纹十次对称二维准晶半平面弹性的无摩擦接触问题.利用十次对称二维准晶位移、应力的复变函数表达式, 带任意形状裂纹的准晶半平面弹性无摩擦接触问题被转换为可解的解析函数复合边值问题，进而简化成一类可解的Riemann边值问题.通过求解Riemann边值问题，得到了应力函数的封闭解, 并给出了裂纹端点处应力强度因子和压头下方准晶体表面任意点处接触应力的显式表达式.从压头下方接触应力的表达式可以看出, 接触应力在压头边缘和裂纹端点处具有奇异性.当忽略相位子场影响时, 该文所得结论与弹性材料对应结果一致.数值算例分别给出了单个平底刚性压头无摩擦压入带单个垂直裂纹和水平裂纹的十次对称二维准晶下半平面的结果.该文所得结论为准晶材料的应用提供了理论参考.
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##### 出版历程
• 收稿日期:  2018-04-20
• 修回日期:  2018-06-24
• 刊出日期:  2019-02-01

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