×

The Erdogan fundamental solution-based hybrid boundary node method for fracture problems. (English) Zbl 1464.74332

Summary: Based on the Erdogan fundamental solutions for infinite cracked plates, a new hybrid boundary node method for linear fracture problems is proposed in this paper. The origin singular intensity factor for the Erdogan fundamental solutions is developed to overcome the singular when the field points are coincided with the source points, and no virtual source points are needed, a new scheme for calculating the origin singular intensity factor for the Erdogan fundamental solutions is developed. Based on the Erdogan fundamental solutions, the zero traction boundary condition on crack surfaces is naturally and strictly satisfied in this method, and no nodes are arranged on the crack surface in the entire calculation process. Based on the Erdogan fundamental solution of stress intensity factor for the mixed mode crack, the stress intensity factor of the present method can be easily interpolated by the Erdogan fundamental solutions. As a result, no complex scheme for calculating stress intensity factor is needed. Based on those theories and methods, the proposed method is further applied to analyze some linear crack problems, and the computational accuracy, convergence rate and the versatility of the present method are demonstrated in details.

MSC:

74S15 Boundary element methods applied to problems in solid mechanics
65N38 Boundary element methods for boundary value problems involving PDEs
74R10 Brittle fracture
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Mukherjee, YX; Mukherjee, S., The boundary node method for potential problems, Int J Num methods Eng, 40, 797-815 (1997) · Zbl 0885.65124
[2] Zhang, JM; Yao, ZH; Li, H., A Hybrid boundary node method, Int J Num methods Eng, 53, 751-763 (2002)
[3] Zhang, JM; Yao, ZH; Masataka, T., The meshless regular hybrid boundary node method for 2-D linear elasticity, Eng Anal Bound Elem, 127, 259-268 (2003) · Zbl 1112.74556
[4] Zhang, JM; Yao, ZH., The regular hybrid boundary node method for three-dimensional linear elasticity, Eng Anal Bound Elem, 28, 525-534 (2004) · Zbl 1130.74492
[5] Zhang, JM; Masataka, T.; Toshiro, M., Meshless analysis of potential problems in three dimensions whit the hybrid boundary node method, Int J Num Meth Eng, 59, 1147-1168 (2004) · Zbl 1048.65121
[6] Zhang, JM; Yao, ZH, Meshless regular hybrid boundary node method, Comput Model Eng Sci, 2, 307-318 (2001) · Zbl 0991.65129
[7] Wang, HT; Yao, ZH; Cen, S., A meshless singular hybrid boundary node method for 2-D elatostatics, J Chin Inst Eng, 27, 481-490 (2004)
[8] Miao, Y.; Wang, YH; Yu, F., An improved hybrid boundary node method in two-dimensional solids, Acta Mech Solida Sin, 18, 307-315 (2005)
[9] Miao, Y.; Wang, Q.; Zhu, HP, Thermal analysis of 3d composites by a new fast multipole hybrid boundary node method, Comput Mech, 53, 77-90 (2014) · Zbl 1398.74058
[10] Miao, Y.; Sun, TC; Zhu, HP; Wang, Q., A new model for the analysis of reinforced concrete members with a coupled HdBNM/FEM, Appl Math Model, 38, 5582-5591 (2014) · Zbl 1428.74219
[11] Yan, F.; Feng, XT; Zhou, H., A dual reciprocity hybrid radial boundary node method based on radial point interpolation method, Comput Mech, 45, 541-552 (2010) · Zbl 1206.74024
[12] Yan, F.; Wang, YH; Tham, LG; Cheung, YK, Dual reciprocity hybrid boundary node method for 2-D elasticity with body force, Eng Anal Bound Elem, 32, 713-725 (2008) · Zbl 1244.74201
[13] Yan, F.; Wang, YH; Miao, Y.; Tan, F., Dual reciprocity hybrid boundary node method for three-dimensional elasticity with body force, Acta Mech Solida Sin, 21, 267-277 (2008)
[14] Nardini, D.; Brebbia, CA., Transient dynamic analysis by the boundary element method, (Boundary element methods in engineering. Southampton: computational mechanics publications (1983), Springer: Springer Berlin and New York) · Zbl 0548.73061
[15] Yan F, Wang YH, Miao Y, Cheung YK. Dual reciprocity hybrid boundary node method for free vibration analysis. J Sound Vib2009; 321: 1036-1057
[16] Yan, F.; Miao, Y.; Yang, QN, Quasilinear hybrid boundary node method for solving nonlinear problems, CMES-Comput Model Eng Sci, 46, 1, 21-50 (2009) · Zbl 1231.65250
[17] Yan, F.; Yu, M.; Lv, JH, Dual reciprocity boundary node method for convection-diffusion problems, Eng Anal Bound Elem, 80, 230-236 (2017) · Zbl 1403.65235
[18] Yan, F.; Feng, XT; Zhou, H., Dual reciprocity hybrid radial boundary node method for the analysis of Kirchhoff plates, Appl Math Model, 35, 12, 5691-5706 (2011) · Zbl 1228.74044
[19] Yan, F.; Feng, XT; Zhou, H., Dual reciprocity hybrid radial boundary node method for Winkler and Pasternak foundation thin plate, Arch Appl Mech, 83, 2, 225-239 (2013) · Zbl 1293.74430
[20] Yan, F.; Pan, PZ; Feng, XT; Li, SJ; Jiang, Q., A fast successive relaxation updating method for continuous-discontinuous cellular automaton method, Appl Math Model, 66, 156-174 (2019) · Zbl 1481.37013
[21] Wang, HB; Yan, F.; Li, XC, Evolution mechanism study of flow-slide catastrophes in large waste dumps at the Nanfen iron mine, B Eng Geol Environ (2020)
[22] Jiang, Quan; Yang, Bing; Yan, Fei, New method for characterizing the shear damage of natural rock joint based on 3d engraving and 3d scanning, Int J Geomech, 20, 2, Article 06019022 pp. (2020)
[23] Yan, F.; Pan, PZ; Feng, XT; Li, SJ, The continuous-discontinuous cellular automaton method for elastodynamics crack problems, Eng Fract Mech, 204, 482-496 (2018)
[24] Yan, F.; Feng, XT; Lv, JH; Pan, PZ, A new hybrid boundary node method based on Taylor expansion and Shepard interpolation method, Int J Numer Meth Eng, 102, 1488-1506 (2015) · Zbl 1352.65600
[25] Neves, AC; Brebbia, CA., The multiple reciprocity method applied to thermal stress problems, Int J Num Meth Eng, 35, 3, 443-455 (1992) · Zbl 0767.73087
[26] Tan, F.; Wang, SF; Lv, JH; Jiao, YY, A Galerkin boundary cover method for viscous fluid flows, Eur J Mech B Fluid, 78, 174-181 (2019) · Zbl 1476.76059
[27] Tan, F.; Wang, YH., Multiple reciprocity hybrid boundary node method for potential problems, Eng Anal Bound Elem, 34, 369-376 (2010) · Zbl 1244.65230
[28] Wang, Q.; Yang, HY., A rigid-inclusion model for fiber-reinforced composites by fast multipole hybrid boundary node method, Eng Anal Bound Elem, 54, 76-85 (2015) · Zbl 1403.74025
[29] Wang, Q.; Miao, Y.; Zhu, HP, A new formulation for thermal analysis of composites by hybrid boundary node method, Int J Heat Mass Transf, 64, 322-330 (2013)
[30] Coifman, R., The fast multipole method for the wave equation: a pedestrian prescription, IEEE Trans Antennas Propag Mag, 35 (1993)
[31] Wang, Q.; Zhou, W.; Feng, YT, The phase-field model with an auto-calibrated degradation function based on general softening laws for cohesive fracture, Appl Math Model, 86, 185-206 (2020) · Zbl 1481.74679
[32] Zhou, W.; Liu, B.; Wang, Q.; Chang, XL; Chen, XD, Formulations of displacement discontinuity method for crack problems based on boundary element method, Eng Anal Bound Elem, 115, 86-95 (2020) · Zbl 1464.74357
[33] Yan, F.; Feng, XT; Lv, JH; Li, SJ, The continuous-discontinuous hybrid boundary node method for solving stress intensity factor, Eng Anal Bound Elem, 81, 35-43 (2017) · Zbl 1403.74256
[34] Chen, W.; Fu, Z.; Wei, X., Potential problems by singular boundary method satisfying moment condition, Comput Model Eng Sci, 54, 65-85 (2009) · Zbl 1231.65245
[35] Wei, X.; Chen, W.; Sun, LL; Chen, B., A simple accurate formula evaluating origin intensity factor in singular boundary method for two-dimensional potential problems with Dirichlet boundary, Eng Anal Bound Elem, 58, 151-165 (2015) · Zbl 1403.65263
[36] Erdogan, F., On the stress distribution in a plate with collinear cuts under arbitrary loads, (Proc. 4th US national congress of applied mechanics (1962)), 547-553
[37] Su, C.; Zheng, C., Calculating of stress intensity factors by boundary element method based on Erdogan fundamental solutions, Chin J Theor Appl Mech, 39, 1, 93-99 (2007)
[38] Yan, F.; Jiang, Q.; Li, SJ; Pan, PZ; Xu, DP; Zhang, JX; Fan, B., A dual singular hybrid boundary node method based on origin singular intensity factor, Eng Anal Bound Elem (2020) · Zbl 1464.65253
[39] Dong, YW; Yu, TT; Ren, QW, Extended finite element method for direct evaluation of strength intensity factors, Chin J Comput Mech, 25, 1, 72-77 (2008) · Zbl 1183.74268
[40] Chang, CC; Mear, ME., A boundary element method for two dimensional linear elastic fracture analysis, Int J Fract, 74, 219-251 (1995)
[41] Pan, E., A general boundary element analysis of 2-D linear elastic fracture mechanics, Int J Fract, 88 (1997), 41-59s
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.