一维六方准晶带裂纹的弹性半平面无摩擦接触问题研究  

On the Frictionless Contact Problem of Elastic Half Plane with Cracks in One-Dimensional Hexagonal Quasicrystals

作　　者：马小丹[1] 李星[1] 赵雪芬[1] 

机构地区：[1]宁夏大学数学统计学院,宁夏银川750021

出　　处：《力学季刊》2017年第2期281-288,共8页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(11362018);宁夏大学自然科学基金(ZR15026);宁夏大学研究生创新项目(GIP201622);宁夏大学新华学院院级科研项目(No.16XHKY01)

摘　　要：利用平面弹性复变函数方法,讨论了工程实际中一维六方准晶带裂纹的弹性半平面无摩擦接触问题.通过合理的应力函数分解,将接触问题归结为解析函数的复合边值问题,进而转化为可解的Riemann边值问题,最后得到封闭形式的解,并给出裂纹尖端的应力强度因子及压头下方接触应力的分布.当不计相位子场及它与声子场的耦合作用时,所得结论可退化为各向同性弹性材料的对应结论,从而验证本文推导的正确性.By using the plane elastic complex variable method, the frictionless contact problem of elastic half-plane with cracks in one-dimensional hexagonal quasicrystals was discussed. Through reasonable stress function decomposition, the problem becomes an analytic function value problem. It is then transformed into Riemann＇s boundary value problem, and finally solved in closed form. The stress intensity factor at the crack tip and the distribution of contact stress under the punch were given. Ignoring the phason field and the phonon-phason coupling effect, the obtained results can be degraded to the corresponding results for isotropic elastic materials, which verifies the correctness of the derivation.

关 键 词：一维六方准晶 裂纹 接触问题 复变函数方法 应力强度因子 

分 类 号：O343[理学—固体力学]