准格林函数方法在弹性扭转问题中的应用  

Application of Green Quasifunction Method in Elastic Torsion

作　　者：王红[1] 袁鸿[2] 

机构地区：[1]广东工业大学建设学院,广东广州510640 [2]暨南大学力学与土木工程系,广东广州510632

出　　处：《华南理工大学学报（自然科学版）》2004年第11期86-88,共3页Journal of South China University of Technology(Natural Science Edition)

基　　金：广东省自然科学基金资助项目 (0 32 4 88)

摘　　要：利用Poisson方程的基本解构造一个准格林函数 ,这个函数满足Poisson方程的齐次边界条件 .应用格林函数将边值问题化为积分方程 ,并通过建立一个规范化的边界方程来表示问题的边界 ,以克服积分方程核的奇异性 .弹性扭转问题可看成是Poisson方程的边值问题 ,R 函数理论保证了对于任何复杂的区域 ,总可以找到一个规范化方程 ,从而可以将弹性扭转问题化为一个无奇异性的第二类Fredholm积分方程 .数值算例表明 ,该方法具有较高的精度 ,可用于力学、物理中复杂边值问题的研究 .In this paper, a Green quasi-function is firstly set up by using the basic solution of Poisson's equation. This function satisfies the homogeneous boundary condition of Poisson's equation. Next, the boundary value problem is changed into an integral equation by applying a Green function. Then, by establishing a normalized boundary equation, the irregularity of the kernel of integral equation is overcome. The elastic torsion can be considered as a boundary value problem of Poisson's equation. For any complicated area, a normalized boundary equation can always be found according to the R-function theory, so the elastic torsion problem can be transformed into a second-class Fredholm integral equation without irregularity. Numerically illustrated results show that the proposed method is of high accuracy and can be used to solve other complicated boundary value problems in mechanics and physics.

关 键 词：格林函数 积分方程 POISSON方程 弹性扭转 

分 类 号：O302[理学—力学] O343.2