Boundary Element Analysis of Interaction Between an Elastic Rectangular Inclusion and a Crack
-
摘要: 使用边界元法研究了无限弹性体中矩形弹性夹杂对曲折裂纹的影响，导出了新的复边界积分方程．通过引入与界面位移密度和面力有关的未知复函数H(t)，并使用分部积分技巧，使得夹杂和基体界面处的面力连续性条件自动满足，而边界积分方程减少为2个，且只具有1/r阶奇异性．为了检验该边界元法的正确性和有效性，对典型问题进行了数值计算．所得结果表明：裂纹的应力强度因子随着夹杂弹性模量的增大而减小，软夹杂有利于裂纹的扩展，而刚性较大的夹杂对裂纹有抑制作用．Abstract: The interaction between an elastic rectangular inclusion and a kinked crack in an infinite elastic body was considered by using boundary element method.The new complex boundary integral equations were derived.By introducing a complex unknown function H(t)related to the interface displacement density and traction and applying integration by parts,the traction continuous condition was satisfied automatically.Only one complex boundary integral equation was obtained on interface and involves only singularity of order 1/r.To verify the validity and effectiveness of the present boundary element method,some typical examples were calculated.The obtained results show that the crack stress intensity factors decrease as the shear modulus of inclusion increases.Thus,the crack propagation is easier near a softer inclusion and the harder inclusion is helpful for crack arrest.
-
Key words:
- kinked crack /
- elastic rectangular inclusion /
- boundary element /
- stress intensity factor
-
[1] WANG Yin-bang,Chau K T.A new boundary element method for plane elastic problems involving cracks and holes[J].International Journal of Fracture,1997,87(1):1—20. doi: 10.1023/A:1007469816603 [2] Chau K T,WANG Yin-bang.Singularity analysis and boundary integral equation method for frictional crack problems in two-dimensional elasticity[J].International Journal of Fracture,1998,90(3):251—274. doi: 10.1023/A:1007422305110 [3] Chau K T,WANG Yin-bang.A new boundary integral formulation for plane elastic bodies containing cracks and holes[J].International Journal of Solids and Structures,1999,36(14):2041—2074. WANG Yin-bang,Chau K T.A new boundary element method for mixed boundary value problems involving cracks and holes:Interactions between rigid inclusions and cracks[J].International Journal of Fracture,2001,110(4):387—406. doi: 10.1016/S0020-7683(98)00078-X [5] WANG Yin-bang.A new boundary integral equation method of three-dimensional crack analysis[J].International Journal of Fracture,1993,63(4):317—328. doi: 10.1007/BF00013041 [6] WANG Yin-bang,CHEN Wei-jiang.Interaction of two equal coplanar square cracks in three-dimensional elasticity[J].International Journal of Solids and Structures,1993,30(23):3315—3320. doi: 10.1016/0020-7683(93)90116-O [7] 王银邦，王海峰.圆形裂纹分析的边界积分方程方法[J].兰州大学学报，1997，33(1)：33—38. [8] 王银邦.非轴对称载荷作用下的外部圆形裂纹问题[J].应用数学和力学，2001，22(1)：9—15. [9] Sih G C.Handbook of Stress-Intensity Factors[M].Bethlehem:Lehigh University,1973. [10] Kitagawa H,Yuuki R,Ohira T.Crack-morphological aspects in fracture mechanics[J].Engineering Fracture Mechanics,1975,7(3):515—529. doi: 10.1016/0013-7944(75)90052-1 [11] Pan E,Amadei B.Fracture mechanics analysis of cracked 2-D anisotropic media with a new formulation of the boundary element method[J].International Journal of Fracture,1996,77(2):161—174. doi: 10.1007/BF00037235 -
计量
- 文章访问数: 2851
- HTML全文浏览量: 138
- PDF下载量: 512
- 被引次数: 0
下载:
渝公网安备50010802005915号