自由边半平面体裂纹问题的超奇异积分方程法  

Hyper-singular Integral Equation Method on Crack in Half-plane Body with Free Boundary

作　　者：杜云海[1] 郭同德[1] 

机构地区：[1]郑州大学工程力学系,河南郑州450002

出　　处：《郑州大学学报（工学版）》2003年第1期28-31,共4页Journal of Zhengzhou University（Engineering Science）

摘　　要：对自由边半平面平行于界面的裂纹问题进行了研究.根据自由边半平面弹性体的弹性力学基本解,利用换功定律、位移-应变关系、胡克定律及裂纹岸应力边界条件,得到描述该问题的超奇异积分方程组,并通过积分变换,在有限部积分的意义下建立了相应的数值方法.对裂纹面上作用均布力情况的算例表明,在自由边附近,即便裂纹面上单独作用法向力或切向力,Ⅰ、Ⅱ型应力强度因子也同时存在,并发生剧烈的变化.The problem of the crack parallel to the free boundary in a half-plane body, with the distributed loads only at the crack surface is discussed in this paper.Based on the fundamental solution of the elastic mechanics on a half-plane body with the free boundary,and using Bitt's law, the stressdisplacement relation, Hooke's law,and stress boundary condition of the crack, the hypersingular integral equations to describe this problem are derived.Through suitable integral transforms,the corresponding numerical method,in the sense of the finitepart integral of the hypersingular integral is established.Using this method, the nondimensional stress intensity factors of the crack under the uniformly distributed loads are calculated.The result shows that Ⅰ,Ⅱ type stress intensity factors exist synchronously, and change greathy,close to the free boundary, even if there is single normal or tangent direction load on the crack boundary. 

关 键 词：自由边半平面体 裂纹 超奇异积分方程 应力强度因子 数值计算 

分 类 号：O346.1[理学—固体力学]