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Li Cong, Niu Zhongrong, Hu Zongjun, Hu Bin. ANALYSIS OF 3-D NOTCHED/CRACKED STRUCTURES BY USING EXTENDED BOUNDARY ELEMENT METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1394-1408. DOI: 10.6052/0459-1879-20-129
Citation: Li Cong, Niu Zhongrong, Hu Zongjun, Hu Bin. ANALYSIS OF 3-D NOTCHED/CRACKED STRUCTURES BY USING EXTENDED BOUNDARY ELEMENT METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1394-1408. DOI: 10.6052/0459-1879-20-129

ANALYSIS OF 3-D NOTCHED/CRACKED STRUCTURES BY USING EXTENDED BOUNDARY ELEMENT METHOD

  • Received Date: April 18, 2020
  • According to the theory of linear elasticity, the conventional numerical methods are difficult to calculate the singular stress fields of three dimensional V-notched/cracked structures because of the stress singularity in the V-notch/crack tip region. In this paper, the extended boundary element method (XBEM) is first proposed to calculate the whole displacement and stress fields of three dimensional V-notch/crack structures. Firstly, the three dimensional V-notched/cracked structure is divided into two parts, which are a small sectoral column around the notch/crack tip and the outer region without the tip sectorial column. The displacement and stress components in the small sector column are expressed as the asymptotic series expansions with respect to the radial coordinate from the tip. The stress singular orders and the associated displacement and stress eigen-functions in the tip region are determined by the interpolating matrix method. The amplitude coefficients in the asymptotic series expansions are taken as the basic unknowns. Secondly, the boundary element method is used to analyze the three dimensional V-notched/cracked structure removed the small sector column. Hence, the whole displacement and stress fields of both the tip region and outer region are obtained by combining the boundary element analysis and the asymptotic series expansions of the displacement and stress fields in the notch/crack tip region, where the XBEM has the characteristics of the semi-analytic approach. The XBEM is suitable for the displacement and stress analysis of the three dimensional V-notched/cracked structures, and its solution can accurately describe the displacement and stress fields from the notch/crack tip to the whole region of the V-notched/cracked structures. Finally, two typical examples are given to demonstrate the effectiveness and accuracy of the extended boundary element method.
  • [1] Chue CH, Liu CI. A general solution on stress singularities in an an-isotropic wedge. International Journal of Solids & Structures, 2001,38(1):6889-6906
    [2] Ungamornrat J. Analysis of 3D cracks in an isotropic multi-material domain with weakly singular SGBEM. Engineering Analysis with Boundary Elements, 2006,30(10):834-846
    [3] Sator C, Becher W. Closed-form solutions for stress singularities at plane bi-and tri-material junctions. Archive of Applied Mechanics, 2012,82(5):643-654
    [4] 胡宗军, 牛忠荣, 程长征. 三维边界元法高阶单元几乎奇异积分半解析算法. 力学学报, 2014,46(3):417-427
    [4] ( Hu Zongjun, Niu Zhongrong, Cheng Changzheng. A new semi-analytic algorithm of nearly singular integrals in high order boundary element analysis of 3D potential. Chinese Journal of Theoretical and Applied Mechanics, 2014,46(3):417-427 (in Chinese))
    [5] Wu W, Lv C, Zhang JH. Interface traction stress of 3D dislocation loop in an isotropic bio-material. Journal of the Mechanics and Physics of Solids, 2016,87(1):7-37
    [6] 文龙飞, 王理想, 田荣. 动载下裂纹应力强度因子计算的改进型扩展有限元法. 力学学报, 2018,50(3):599-610
    [6] ( Wen Longfei, Wang Lixiang, Tian Rong. Accurate computation on dynamic SIFS using improved XFEM. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(3):599-610 (in Chinese))
    [7] Xu CH, Qin TY, Noda NA. Numerical solutions of singular integral equations for planar rectangular interfacial crack in three dimensional bio-materials. Applied Mathematics and Mechanics, 2007,28(6):751-757
    [8] 王振, 余天堂. 模拟三维裂纹问题的自适应多尺度扩展有限元法. 工程力学, 2016,33(1):32-38
    [8] ( Wang Zhen, Yu Tiantang. Adaptive multi scale extended finite element method for modeling three-dimensional crack problems. Engineering Mechanics, 2016,33(1):32-38 (in Chinese))
    [9] 贾旭, 胡绪腾, 宋迎东. 基于三维裂纹尖端应力场的应力强度因子计算方法. 航空动力学报, 2016,31(6):1417-1426
    [9] ( Jia Xu, Hu Xuteng, Song Yingdong. Calculation method of stress intensity factor based on the three-dimensional stress field at the crack tip. Journal of Aerospace Power, 2016,31(6):1417-1426 (in Chinese))
    [10] Fakoor M, Ghoreishi SMN. Comprehensive investigation of stress intensity factors in rotating disks containing three-dimensional semi-elliptical cracks. Applied Mathematics and Mechanics, 2017,38(1):1565-1578
    [11] Huang T, Zheng JL, Lv ST, et al. Failure criterion of an asphalt mixture under three-dimensional stress state. Construction and Building Materials, 2018,170(1):708-715
    [12] 贾旭, 胡绪腾, 宋迎东. 复杂载荷应力强度因子的计算方法. 航空动力学报, 2018,33(6):1464-1474
    [12] ( Jia Xu, Hu Xuteng, Song Yingdong. Calculation method of stress intensity factors of eccentric through cracks subjected to complex loading. Journal of Aerospace Power, 2018,33(6):1464-1474 (in Chinese))
    [13] Magnus WG. A 3D model of hydraulic fracturing and micro-seismicity in anisotropic stress fields. Aeromechanics and Geophysics for Geo-Energy and Geo-Resources, 2018,5(1):17-35
    [14] Dhanesh N, Kapuria S, Achary GGS. Accurate prediction of three-dimensional free edge stress field in composite laminates using mixed-field multitier extended Kantorovich method. Acta Mechanica, 2016,228(8):1-25
    [15] Stasyuk B. Interacting cracks 3D analysis using boundary integral equation method. Aims Materials Science, 2016,3(4):1796-1810
    [16] Karsten K, Günther K. The advanced simulation of fatigue crack growth in complex 3D structures. Archive of Applied Mechanics, 2006,76(11-12):699-709
    [17] Li Z, Guo W. Three-dimensional elastic stress fields ahead of blunt V-notches in finite thickness plates. International Journal of Fracture, 2001,107(1):53-71
    [18] Park JH, Nikishkov GP. Growth simulation for 3D surface and through thickness cracks using SGBEM-FEM alternating method. Journal of Mechanical Science & Technology, 2011,25(9):2335-2344
    [19] Lan W, Deng X, Sutton MA. Three-dimensional finite element simulations of mixed-mode stable tearing crack growth experiments. Engineering Fracture Mechanics, 2007,74(16):2498-2517
    [20] Dias IF, Oliver J, Lloberas VO. Strain-injection and crack-path field techniques for 3D crack-propagation modeling in quasi-brittle materials. International Journal of Fracture, 2018,212(1):67-87
    [21] Ding P, Wang X. Three-dimensional mixed-mode (I and II) crack-front fields in ductile thin plates effects of T--stress. Fatigue & Fracture of Engineering Materials & Structures, 2017,40(1):349-363
    [22] Wang H, Cao M, Siddique A, et al. Numerical analysis of thermal expansion behaviors and interfacial thermal stress of 3D braided composite materials. Computational Materials Science, 2017,138(1):77-91
    [23] 李聪, 牛忠荣, 胡宗军 等. 求解双材料裂纹结构全域应力场的扩展边界元分法. 应用数学与力学, 2019,40(8):909-920
    [23] ( Li Cong, Niu Zhongrong, Hu Zongjun, et al. Computation of total stress fields for cracked Bi-Material structure with the extended boundary element method. Applied Mathematics and Mechanics, 2019,40(8):909-920 (in Chinese))
    [24] Li C, Niu ZR, Hu ZJ, et al. Effectiveness of the stress solutions in notch/crack tip regions by using extended boundary element method. Engineering Analysis with Boundary Elements, 2019,108(1):1-13
    [25] Yosibash Z, Szabó BA. A note on numerically computed eigen-functions and generalized stress intensity factors associated with singular points. Engineering Fracture Mechanics, 1996,54:593-595
    [26] Williams ML. Stress singularities resulting from various boundary conditions in angular corners of plates in tension. Journal of Applied Mechanics, 1952,19:526-528
    [27] Niu ZR, Ge DL, Cheng CZ, et al. Evaluation of the stress singularities of plane V-notches in bonded dissimilar materials. Applied Mathematical Modeling, 2009,33(1):1776-1792
    [28] 程长征, 葛仁余, 牛忠荣 等. 三维切口应力奇性指数计算. 固体力学学报, 2012,33(6):623-629
    [28] ( Cheng Changzheng, Ge Renyu, Niu Zhongrong, et al. Evaluation of the stress singularity order for three-dimensional V-notch. Chinese Journal of Solid Mechanics, 2012,33(6):623-629 (in Chinese))
    [29] 钱俊, 龙驭球. 三维切口尖端应力应变场. 应用力学与数学, 1994,15(3):199-208
    [29] ( Qian Jun, Long Yuqiu. The expression of stress and strain at the tip of three dimensional notch. Applied Mathematics and Mechanics, 1994,15(3):199-208 (in Chinese))
    [30] 牛忠荣, 王秀喜, 周焕林. 三维边界元法中几乎奇异积分的正则化算法. 力学学报, 2004,36(1):49-56
    [30] ( Niu Zhongrong, Wang Xiuxi, Zhou Huanlin. A regularization algorithm for the nearly singular integrals in 3-D BEM. Chinese Journal of Theoretical and Applied Mechanics, 2004,36(1):49-56 (in Chinese))
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