| 带裂纹十次对称二维准晶平面弹性的无摩擦接触问题 |
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| 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. |
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| 作者姓名： | 赵雪芬 李星 |
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| 作者单位： | 1宁夏大学新华学院, 银川 750021;2宁夏大学 数学统计学院, 银川 750021 |
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| 基金项目： | 宁夏自然科学基金（NZ17042）；国家自然科学基金(11762017) |
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| 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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| 关 键 词： | 十次对称二维准晶 无摩擦接触问题 裂纹 边值问题 应力强度因子 |
| 收稿时间： | 2018-04-20 |
A Frictionless Contact Problem of 2D Decagonal Quasicrystal Plane Elasticity With Cracks |
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| Affiliation: | 1Xinhua College of Ningxia University, Yinchuan 750021, P.R.China;2School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, P.R.China |
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| Abstract: | With the classical complex function method, a frictionless contact problem of 2D decagonal quasicrystal semi plane elasticity with arbitrary form cracks was addressed under the action of a rigid convex basal punch. Based on complex expressions of stresses and displacements of 2D decagonal quasicrystals, the problem was converted into solvable boundary value problems with analytic functions, and then reduced to a class of Riemann boundary problems. Solutions to the Riemann boundary problems give the stress functions in closed form, the explicit expressions of the stress intensity factors at crack tips and the contact stress distribution under the punch. The expression of the contact stress shows that, it has singularity at the edge of the contact zone and the crack tips. Without the effect of the phason field, the obtained results match well with those classical conclusions for elastic materials. Numerical examples illustrated the solutions to the frictionless contact problem in 2D decagonal quasicrystal semi plane elasticity with a vertical crack and a horizontal straight crack under a rigid punch. The work provides a theoretical reference for the application of quasicrystalline materials. |
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