全空间中粒子和裂纹的对偶边界积分方程及数值解

doi:10.3969/j.issn.1007-2861.2015.02.020

Abstract

Abstract:

As elastic solids contain particles and cracks, a computational model is proposed for the analysis of particles and cracks in full space using dual boundary integral equations in the displacement discontinuity formulation. The method avoids the difficulty of loading the objects under study in full space. Numerical analysis is carried out for some typical cases with a few particles and cracks using a discrete form of boundary integral equations. A boundary point method and Gauss collocation are used for discretization of the particle boundary or interface, and the crack surface, respectively. The stress intensity factors of cracks are computed. Mutual effects between particles and cracks are investigated and compared with those in the literature, verifying correctness and reliability of the proposed computational model and the program.

Key words: numerical solution , dual boundary integral equation , stress intensity factor, crack , particle

MA Hang1, PAN Meng2. Dual boundary integral equations and numerical solutions for particles and cracks in full space[J]. Journal of Shanghai University（Natural Science Edition）, 2016, 22(5): 533-544.

References

[1] Aliabadi M H, Rooke D P. Numerical fracture mechanics [M]. Southampton: Computational Mechanics Publications, 1991: 140-192.
[2] Cruset A. Boundary element analysis in computational fracture mechanics [M]. Dordrecht: Kluwer Academic Publishers, 1988: 17-60.
[3] 黎在良, 王元汉, 李廷芥. 断裂力学中的边界数值方法[M]. 北京: 地震出版社, 1996: 237-265.
[4] Yan X Q. Stress intensity factors for cracks emanating from a triangular or square hole in an infinite plateby boundary elements [J]. Engineering Failure Analysis, 2005, 12(3): 362-375.
[5] Yan X Q. A brief evaluation of approximation methods for microcrack shielding problems [J]. ASME Journal of Applied Mechanics, 2006, 73(4): 694-696.
[6] Ma H, Guo Z G, Dhanasekar M, et al. Efficient solution of multiple cracks in great number using eigen COD boundary integral equations with iteration procedure [J]. Engineering Analysis with Boundary Elements, 2013, 37(3): 487-500.
[7] Guo Z, Liu Y, Ma H, et al. A fast multipole boundary element method for modeling 2-D multiple crack problems with constant elements [J]. Engineering Analysis with Boundary Elements, 2014, 47(1): 1-9.

[8] Dong C Y, Cheung Y K, Lo S H. An integral equation approach to the inclusion-crack interactions in three-dimensional infinite elastic domain [J]. Computational Mechanics, 2002, 29(4/5): 313-321.
[9] Dong C Y, Lo S H, Cheung Y K. Numerical analysis of the inclusion-crack interactions using an integral equation [J]. Computational Mechanics, 2003, 30(2): 119-130.
[10] Dong C Y, Leek Y. A new integral equation formulation of two-dimensional inclusion-crack problems [J]. International Journal of Solids and Structures, 2005, 42(18/19): 5010-5020.
[11] Dong C Y, Lee K Y. Boundary element analysis of infinite anisotropic elastic medium containing inclusions and cracks [J]. Engineering Analysis with Boundary Elements, 2005, 29(6): 562-569.
[12] Dong C Y. The integral equation formulations of an infinite elastic medium containing inclusions, cracks and rigid lines [J]. Engineering Fracture Mechanics, 2008, 75(13): 3952-3965.
[13] Dong C Y, Yang X, Pan E. Analysis of cracked transversely isotropic and inhomogeneous solids by a special BIE formulation [J]. Engineering Analysis with Boundary Elements, 2011, 35(2): 200-206.
[14] Chen Y Z. Boundary integral equation method for two dissimilar elastic inclusions in an infinite plate [J]. Engineering Analysis with Boundary Elements, 2012, 36(1): 137-146.
[15] Ma H, Zhou J, Qin Q H. Boundary point method for linear elasticity using constant and quadratic moving elements [J]. Advances in Engineering Software, 2010, 41(3): 480-488.
[16] Telles J C F, Castor G S, Guimaraes S. A numerical Green’s function approach for boundary elements applied to fracture mechanics [J]. International Journal for Numerical Methods in Engineering, 1995, 38(19): 3259-3274.
[17] Hui C Y, Shia D. Evaluations of hypersingular integrals using Gaussian quadrature [J]. International Journal for Numerical Methods in Engineering, 1999, 44(2): 205-214.
[18] Murakami Y, Keer L M. Stress intensity factors handbook [J]. Journal of Applied Mechanics, 1993, 60(4): 1063.

Dual boundary integral equations and numerical solutions for particles and cracks in full space

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	WANG Tianyu, YANG Xiao. Nonlinear vibration of beam with breathing crack [J]. Journal of Shanghai University（Natural Science Edition）, 2020, 26(3): 443-455.
[2]	Yuan DAI, Tianyu WANG, Xiao YANG. Vibration analysis of cracked beam based on crack's equivalent rotational spring model [J]. Journal of Shanghai University（Natural Science Edition）, 2019, 25(6): 965-977.
[3]	Zhenyu NIU, Zhewei ZHOU, Kai HUANG, Jinsong ZHANG, Jianhua ZHANG, Zhiliang WANG. Laser-induced aggregation of Rayleigh granular jets [J]. Journal of Shanghai University（Natural Science Edition）, 2019, 25(5): 754-766.
[4]	Yu SHANG, Tiantian WANG, Meiying WU, Lu WANG, Huixin HE, Jing AN. Cytotoxicity in SH-SY5Y cells induced by $O_{3}$-oxidized black carbon particles [J]. Journal of Shanghai University（Natural Science Edition）, 2019, 25(4): 550-557.
[5]	GAO Junli, LI Houwei, CAO Wei. Experimental research and numerical simulation of interface between ribbed geomembrane and geotextile [J]. Journal of Shanghai University（Natural Science Edition）, 2019, 25(2): 317-327.
[6]	TU Weiping, LI Chunxiang. Short-term wind pressure forecast using LSSVM based on hybrid intelligent algorithm optimization [J]. Journal of Shanghai University（Natural Science Edition）, 2019, 25(2): 347-356.
[7]	YANG Xiao, MENG Zhe, HUANG Jin. Static parameter identification of cantilever cracked beam with nonholonomic constraint boundary [J]. Journal of Shanghai University（Natural Science Edition）, 2019, 25(1): 120-131.
[8]	LU Shaoke, XIA Xiaohe, ZHANG Mengxi, YANG Jimang. Triaxial analysis of particle flow in geocell reinforced sand samples [J]. Journal of Shanghai University（Natural Science Edition）, 2019, 25(1): 132-140.
[9]	XU Yi, MAO Xinjian, GUO Siyu, FENG Jian. Self-assembly behaviors of zwitterionic heterogemini surfactant in aqueous solution: a dissipative particle dynamics simulation [J]. Journal of Shanghai University（Natural Science Edition）, 2018, 24(6): 912-924.
[10]	YANG Xiao, CHENG Bowei, JIANG Zhiyun. Bending deformation of viscoelastic cracked beam reinforced with fiber reinforcement polymer [J]. Journal of Shanghai University（Natural Science Edition）, 2018, 24(6): 978-992.
[11]	XU Yanqin, LI Chunxiang. Predicting fluctuating wind velocity using optimized combined kernel functions based LSSVM [J]. Journal of Shanghai University（Natural Science Edition）, 2018, 24(4): 627-633.
[12]	WANG Han, ZHOU Zhewei, ZHANG Jinsong, ZHANG Jianhua, WANG Zhiliang. Attenuation characteristics of Gaussian beams passing through a granular system [J]. Journal of Shanghai University（Natural Science Edition）, 2018, 24(3): 392-401.
[13]	LIU Feiyu, ZHANG Duanyang, WANG Jun. Cyclic and post-cyclic direct shear behavior of sandwich reinforcement-soil interface under different sand particle sizes [J]. Journal of Shanghai University（Natural Science Edition）, 2018, 24(3): 456-466.
[14]	QI Gongmin, DI Zengfeng, REN Wei. Photoelectric-response enhancement of local surface plasmon in Ge [J]. Journal of Shanghai University（Natural Science Edition）, 2018, 24(2): 207-216.
[15]	ZHANG Zhimei, ZHANG Zhenkai, XIONG Hao, WANG Zhuo, CHEN Gang. Method of bond-slip model of near-surface mounted FRP strips-concrete interfaces [J]. Journal of Shanghai University（Natural Science Edition）, 2018, 24(2): 304-313.