An Effective Boundary Element Method for Analysis of Crack Problems in a Plane Elastic Plate
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摘要: 提出了一种简单而有效的平面弹性裂纹应力强度因子的边界元计算方法.该方法由Crouch与Starfield建立的常位移不连续单元和闫相桥最近提出的裂尖位移不连续单元构成A·D2在该边界元方法的实施过程中,左、右裂尖位移不连续单元分别置于裂纹的左、右裂尖处,而常位移不连续单元则分布于除了裂尖位移不连续单元占据的位置之外的整个裂纹面及其它边界.算例(如单向拉伸无限大板中心裂纹、单向拉伸无限大板中圆孔与裂纹的作用)说明平面弹性裂纹应力强度因子的边界元计算方法是非常有效的.此外,还对双轴载荷作用下有限大板中方孔分支裂纹进行了分析.这一数值结果说明平面弹性裂纹应力强度因子的边界元计算方法对有限体中复杂裂纹的有效性,可以揭示双轴载荷及裂纹体几何对应力强度因子的影响.Abstract: A simple and effective boundary element method for stress intensity factor calculation for crack problems in a plane elastic plate is presented.The boundary element method consists of the constant displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity elements proposed by YAN Xiao-qiao.In the boundary element implementation the left or the right crack-tip displacement discontinuity element was placed locally at the corresponding left or right each crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries.Test examples (i.e.,a center crack in an infinite plate under tension,a circular hole and a crack in an infinite plate under tension) are included to illustrate that the numerical approach is very simple and accurate for stress intensity factor calculation of plane elasticity crack problems.In addition,specifically,the stress intensity factors of branching cracks emanating from a square hole in a rectangular plate under biaxial loads were analysed.These numerical results indicate the present numerical approach is very effective for calculating stress intensity factors of complex cracks in a 2-D finite body,and are used to reveal the effect of the biaxial loads and the cracked body geometry on stress intensity factors.
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[1] Cruse T A.Numerical evaluation of elastic stress intensity factors by boundary integral equation method[A].In:Swedlow J L Ed.Surface Cracks Physics Problems and Computational Solutions[C].New York:ASME,1972,153—170. [2] Cruse T A.Two dimensional BIE fracture mechanics analysis[J].Appl Math Modeling,1978,2(3):287—293. doi: 10.1016/0307-904X(78)90023-9 [3] Blandford G E,Ingraffea A R,Liggett J A.Two-dimensional stress intensity factor computations using the boundary element method[J].Internat J Numer Methods Engrg,1981,17(4):387—404. doi: 10.1002/nme.1620170308 [4] Crouch S L,Starfield A M.Boundary Element Method in Solid Mechanics[M]. London:Geore Allon & Unwin,1983,79—109. [5] Pan E.A general boundary element analysis of 2-D linear elastic fracture mechanics[J].Internat J Fracture,1997,28(1):41—59. [6] Portela A,Aliabadi M H,Rook D P. The dual boundary element method: effective implementation for crack problems[J].Internat J Numer Methods Engrg,1992,33(12):1269—1287. doi: 10.1002/nme.1620330611 [7] Mi Y,Aliabadi M H.Dual-boundary element method for three dimensional fracture mechanics analysis[J].Engineering Analysis With Boundary Elements,1992,10(2):161—171. doi: 10.1016/0955-7997(92)90047-B [8] Tanaka M,Itoh H.New crack elements for boundary element analysis of elastostatics considering arbitrary stress singularities[J].Appl Math Modelling, 1987,11(4):357—363. doi: 10.1016/0307-904X(87)90030-8 [9] Cruse T A.Boundary Element Analysis in Computational Fracture Mechanics[M].Dordrecht: Kluwer,1989,1—120. [10] Aliabadi M H,Rooke D P.Numerical Fracture Mechanics[M].Southampton: Computational Mechanics Publications and Dordrecht: Kluwer, 1991,1—150. [11] Aliabadi M H.Boundary element formulation in fracture mechanics[J].Applied Mechanics Review,1997,50(1):83—96. doi: 10.1115/1.3101690 [12] YAN Xiang-qiao.A special crack-tip displacement discontinuity element[J].Mechanics Research Communications,2004,31(6):651—659. doi: 10.1016/j.mechrescom.2004.05.001 [13] Kitagawa H,Yuuki R.Analysis of the non-linear shaped cracks in a finite plate by the conformal mapping method[J].Trans Japan Soc Mech Engrs,1977,43(376):4354—4362. doi: 10.1299/kikai1938.43.4354 [14] Murakami Y.A method of stress intensity factor calculation for the crack emanating from an arbitrarily shaped hole or the crack in the vicinity of an arbitrarily shaped hole[J].Trans Japan Soc Mech Engrs,1978,44(378):423—432. doi: 10.1299/kikai1938.44.423 [15] Murakami Y.Stress Intensity Factors Handbook[M].New York;Pergamon Press,1987,266—267. [16] Erdogan F,Gupta G D,Ratwani M.Interaction between a circular inclusion and an arbitrarily oriented crack[J].ASME J Appl Mech,1974,41(6):1007—1013. doi: 10.1115/1.3423424
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