Numerical Simulation of 2D Fiber-Reinforced Composites Using Boundary Element Method
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摘要: 将含有随机分布多种夹杂相复合材料的二维弹性力学问题归结为复连通区域的边界积分方程，进而转化成矩阵方程进行求解和分析．根据同类夹杂相外在边界上的面力与位移之间关系矩阵完全相同的特点，使得最后的矩阵方程阶数得到大规模减少，这正是此处提出改进的边界元方法的主要思路．数值算例表明，对于此类问题，与常规的边界元分域解法相比更加有效．以该方法为基础，可以详细给出纤维增强复合材料二维条件下的宏观等效力学性质．Abstract: The boundary element method was improved for the 2D elastic composites with randomly distributed inclusions.This problem can be reduced to a boundary integral equation for a multi-connected domain.Further,considering the matrices of the tractions and displacements for each group of the identical inclusion were the same,an effective computational scheme was designed,since the orders of the resulting matrix equations can be greatly reduced.Numerical examples indicate that this boundary element method scheme is more effective than the conventional multi-domain boundary element method for such a problem.The present scheme can be used to investigate the effective mechanical properties of the fiber-reinforced composites.
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Key words:
- inclusion /
- boundary element method /
- 2D elasticity /
- fiber-reinforced composite
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[1] Eshelby J D.The determination of the elastic field of an ellipsoidal inclusion and related problems[J].Proc Royal Soc London A,1957,241(1226):376—396. doi: 10.1098/rspa.1957.0133 [2] Hashin Z.The elastic moduli of heterogeneous materials[J].J Appl Mech,1962,29(1):143—150. doi: 10.1115/1.3636446 [3] Budiansky Y.On the elastic moduli of heterogeneous materials[J].J Mech Phys Solids,1965，13(4):223—227. doi: 10.1016/0022-5096(65)90011-6 [4] Hill R.A Self-consistent mechanics of composite materials[J].J Mech Phys Solids,1965,13(4):213—222. doi: 10.1016/0022-5096(65)90010-4 [5] Christensen R M,Lo K H.Solutions for effective shear properties in three phase sphere and cylinder models[J].J Mech Phys Solids,1979,27(4):315—330. doi: 10.1016/0022-5096(79)90032-2 [6] Aboudi J, Benveniste Y.The effective moduli of cracked bodies in plane deformation[J].Engng Fracture Mech，1987，26(2):171—84. doi: 10.1016/0013-7944(87)90195-0 [7] Mori T, Tanaka K. Average stress in matrix and average elastic energy of materials with mis-fitting inclusions[J].Acta Metall，1973，21(4):571—583. doi: 10.1016/0001-6160(73)90064-3 [8] Isida M, Igawa H.Analysis of zig-zag array of circular holes in an infinite solid under uniaxial tension[J].Int J Solids Struc,1991，27(7):849—864. doi: 10.1016/0020-7683(91)90020-G [9] Day A R,Snyder K A,Garboczi E J,et al.The elastic moduli of a sheet containing circular holes[J].J Mech Phys Solids,1992,40(5):1031—1051. doi: 10.1016/0022-5096(92)90061-6 [10] HU Ning,WANG Bo,TAN Guo-wen,et al.Effective elastic properties of 2-D solids with circular holes: numerical simulations[J].Composites Science and Technology,2000,60(9):1811—1823. doi: 10.1016/S0266-3538(00)00054-3 [11] KONG Fan-zhong,YAO Zhen-han,ZHENG Xiao-ping.BEM for simulation of a 2D elastic body with randomly distributed circular inclusions[J].Acta Mechanica Solida Sinica,2002,15(1):81—88. -
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