周期法向载荷下一维六方准晶非周期平面的裂纹问题
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摘要
应用一维六方准晶非周期平面线弹性力学理论,提出被周期直裂纹削弱的一维六方准晶非周期平面的第一基本问题,通过借鉴并改进经典弹性力学中周期弹性平面理论的方法和技巧,对问题进行求解.取特殊情况,得到了周期法向对称载荷下及周期均匀法向对称载荷下的应力函数.
In the linear elasticity framework,the first basic problem of a periodic plane in the onedimensional hexagonal quasicrystals which is weakened by aperiodic horizontal cracks is presented.The problem is solved by referring and improving the method and technique of the periodic elastic plane theory in the classical elasticity theory.In the special cases,the stress functions of periodic normal symmetrical load and uniform normal symmetrical load are obtained.
In the linear elasticity framework,the first basic problem of a periodic plane in the onedimensional hexagonal quasicrystals which is weakened by aperiodic horizontal cracks is presented.The problem is solved by referring and improving the method and technique of the periodic elastic plane theory in the classical elasticity theory.In the special cases,the stress functions of periodic normal symmetrical load and uniform normal symmetrical load are obtained.
引文
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[20]崔江彦,张保文,李星.周期切向载荷下一维六方准晶非周期平面的裂纹问题[J].宁夏大学学报:自然科学版,2016,37(4):385-390.
[2]FIKAR J.Al-Cu-Fe quasicrystalline coatings and composites studied by mechanical spectroscopy[D].Paris:Ecole Polytechnique Federale de Lausanne,2002.
[3]DUBOIS J M.So useful,those quasicrystals[J].Israel Journal of Chemistry,2011(11/12):1168-1175.
[4]PENG Yanze,FAN Tianyou.Crack and indentation problems for one-dimensional hexagonal quasicrystals[J].The European Physical Journal:B,2001,21(1):39-44.
[5]ZHOU Wangmin,FAN Tianyou,YIN Shuyuan,et al.Anti plane elasticity problem and modeⅢcrack problem of cubic quasicrystal[J].Journal of Beijing Institute of Technology,2001,10(1):3250-3254.
[6]刘官厅.弹性与断裂力学复变方法研究进展[J].力学与实践,2010,32(3):10-15.
[7]刘官厅,何青龙,郭瑞平.一维六方准晶非周期平面内的平面应变理论[J].物理学报,2009,58(S1):S118-S123.
[8]范天佑.准晶数学弹性理论及其应用[M].北京:北京理工大学出版社,1999:24-36.
[9]范天佑.准晶数学弹性力学和缺陷力学[J].力学进展,2000,30(2):161-174.
[10]FAN Tianyou.Mathematical theory of elasticity of quasicrystals and its applications[M].Beijing:Science Press,2010:56-79.
[11]王省哲,怡晓玲.弹性力学问题复变函数解法的应用与发展[J].力学与实践,2009,30(6):110-113.
[12]路见可,蔡海涛.平面弹性周期问题概论[M].武汉:武汉大学出版社,2008:46-60.
[13]CAI Haitao,LU Jianke.First fundamental problems of anisotropic elastic plane weakened by periodic collinear cracks[J].Applied Mathematics and Mechanics,2009,30(11):1341-1348.
[14]时朋朋,李星.含双周期裂纹的一维六方准晶电弹性全平面应变基本问题[J].应用力学学报,2014,31(2):251-256.
[15]时朋朋,崔江彦,李星.一维六方准晶非周期半平面的第一周期基本问题[J].工程数学学报,2014,31(4):545-556.
[16]崔江彦,李星,张保文.一维六方准晶材料中双周期裂纹反平面问题[J].宁夏大学学报:自然科学版,2014,35(4):294-298.
[17]崔江彦,李星,安震海.周期载荷下一维六方准晶非周期半平面的第二基本问题[J].宁夏大学学报:自然科学版,2015,36(2):97-102.
[18]杨娟,李星,丁生虎.一维六方压电准晶中带三条不对称裂纹的圆形孔口的反平面问题[J].工程数学学报,2016,33(2):184-198.
[19]于静.含复杂缺陷一维六方压电准晶的断裂问题[J].内蒙古师范大学学报,2016,45(1):4-8.
[20]崔江彦,张保文,李星.周期切向载荷下一维六方准晶非周期平面的裂纹问题[J].宁夏大学学报:自然科学版,2016,37(4):385-390.