含Ⅰ型裂纹八次对称二维准晶动力学问题的数值模拟  

The Numerical Simulation in the Dynamics Problems of Mode Ⅰ Crack in 2D Octagonal Quasicrystals

作　　者：王雅楠 李联和[1,2] 王桂霞 胡学佳[1] WANG Ya-nan;LI Lian-he;WANG Gui-xia;HU Xue-jia(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China;Inner Mongolia Center of Applied Mathematics,Hohhot 010022,China)

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022 [2]内蒙古自治区应用数学中心,内蒙古呼和浩特010022

出　　处：《内蒙古师范大学学报（自然科学版）》2022年第2期147-155,共9页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11962026);内蒙古自治区自然科学基金资助项目(2019LH01001,2020MS01018);内蒙古自治区高校科研资助项目(NJZZ21003,NJZY21570);内蒙古师范大学研究生科研创新基金资助项目(CXJJS20088)。

摘　　要：基于波动—电报模型,利用有限差分法构造了混合精度的离散格式,求解了带Ⅰ型Griffith裂纹的八次对称准晶动力学问题,并对离散格式进行了误差估计和稳定性分析。通过数值实例展示了位移及应力随时间的变化规律,探究了有效质量密度以及摩擦系数对相位子场位移的影响。Based on the wave-telegraph model,a mixed-precision discrete scheme is constructed by using the finite difference method to solve the problem of 2D octagonal quasicrystals with mode Ⅰ crack in the paper.The accuracy and stability are analyzed for the discrete scheme and the variation of displacement and stress with time is displayed by numerical examples. Furthermore,the effect of effective mass density and friction coefficient on the displacement of phase subfield is investigated.

关 键 词：八次对称准晶 Ⅰ型裂纹 波动—电报模型 有限差分 

分 类 号：O214.8[理学—概率论与数理统计]