工程中一类拼接问题的复变方法  

Complex Variable Method for a Class of Bonding Problem on Engineering

作　　者：黄民海[1] 

机构地区：[1]肇庆学院数学系,广东肇庆526061

出　　处：《应用数学》2004年第2期322-327,共6页Mathematica Applicata

基　　金：广东省自然科学基金资助项目 (0 10 4 46 )

摘　　要：讨论工程中一类含边裂缝弹性材料补强的拼接问题 .根据平面弹性复变方法 ,问题归结为一类解析函数的边值问题 ,通过有效的分析方法和积分变换 ,进一步将问题简化为一类奇异积分方程 ,证明了方程解的存在唯一 ,并对方程解的简化进行了研究 ,得到了弹性材料体内应力分布的封闭形式解 。In this paper,a class of bonding problem of elastic materials reinforcing with a boundary crack on engineer is studied.One proper mathematical model is developed and the problem is transfered to a boundary value problem for analytic functions and then further reduced to a singular integral equation,the existence and unique solvability of which is proved mathematically.The reduction of the solution is discussed and the stress distribution of elastic materials body is given in closed forms.The general expression of stress intersity factors is also derived in case of a straight crack.

关 键 词：拼接问题 弹性材料 材料补强 平面弹性复变法 边值问题 奇异积分方程 应力分布 断裂力学 

分 类 号：O346.1[理学—固体力学] O175.5[理学—力学]