螺旋位错与弹性椭圆夹杂干涉问题的一般解答  

Genneral Solution to Interaction Between Screw Dislocation and Elastic Elliptical Inhomogeneity

作　　者：刘又文[1] 宁志华[1] 蒋持平[2] 

机构地区：[1]湖南大学工程力学系,湖南长沙410082 [2]北京航空航天大学飞行器设计与应用力学系,北京100083

出　　处：《湖南大学学报（自然科学版）》2002年第5期14-19,24,共7页Journal of Hunan University:Natural Sciences

基　　金：国家自然科学基金资助项目 ( 19972 0 0 5)

摘　　要：获得反平面一般荷载下 ,弹性椭圆夹杂问题的精确解 ,将复变函数的分区全纯函数理论 ,Cauchy型积分 ,应力函数的奇性主部分析 ,Rie-mann边值问题相结合 ,求得了各复势函数之间的解析关系 ,并将问题归结为一个初等复势函数方程的求解 .在一般荷载下获得级数形式精确解 ;在若干特殊情形下获得封闭形式解 .求出了由夹杂引起的干涉能及位错干涉力的解析表达式 ,并绘出了干涉力的变化曲线 ,研究了位错力随位错方位的变化规律 .解答的特殊情形与已有若干文献结果一致 ,并纠正了其中的一个错误结果 .A percise solution to the elastic elliptical inhomogeneity problem under general antiplane loads was provided.By combining the theory of sectionally holomorphic function,Cauchy model integral,the analysis of the singularity of complex stress function and Riemann boundary problem,the analysis relation between the complex potentials was obtained,and then the problem was transformed into solving an elementary complex potentials equation.The precise solution in series form under general loads andthe several typical solutions in closed form were provided.The interaction energy due to the presence of an elliptical inhomogeneity is formulated.The force acting on the dislocation is provided in form of formulation and figures, the particular discussion is given to its variation with the dilocation azimuth.The typical solutions are the same as those existent,and a mistake in a reference is corrected.

关 键 词：弹性椭圆夹杂 反平面问题 复变函数方法 螺旋位错 复合材料 材料力学 干涉能 干涉力 

分 类 号：O343.7[理学—固体力学]