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Analysis of 2-D elastic solid with multiple V-notches by a fast multipole BEM with a novel singular element with multi-order asymptotic terms. (English) Zbl 1510.65306


MSC:

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

References:

[1] Henshell, R. D.; Shaw, K. G., Crack tip finite elements are unnecessary, Int. J. Numer. Methods Eng., 9, 495-507 (1975) · Zbl 0306.73064
[2] Barsoum, R. S., Further application of quadratic isoparametric finite elements to linear fracture mechanics of plate bending and general shells, Int. J. Numer. Methods Eng., 11, 1, 167-169 (1975)
[3] Banks-Sills, L.; Sherman, D., On quarter-point three-dimensional finite elements in linear elastic fracture mechanics, Int. J. Fract., 41, 3, 177-196 (1989)
[4] Benzley, S. E., Representation of singularities with isoparametric finite elements, Int. J. Numer. Methods Eng., 8, 3, 537-545 (1974) · Zbl 0282.65087
[5] Biggers, S. B.; Pageau, S. S., Enrichment of finite elements with numerical solutions for singular stress fields, Int. J. Numer. Methods Eng., 40, 14, 2693-2713 (1997) · Zbl 0908.73079
[6] Ayhan, A. O., Stress intensity factors for three-dimensional cracks in functionally graded materials using enriched finite elements, Int. J. Solids Struct., 44, 25-26, 8579-8599 (2007) · Zbl 1167.74431
[7] Wu, J. Y., Unified analysis of enriched finite elements for modeling cohesive cracks, Comput. Meth. Appl. Mech. Eng., 200, 45, 3031-3050 (2011) · Zbl 1230.74202
[8] Tong, P.; Pian, T. H H.; Lasry, S. J., A hybird-element approach to crack problems in plane elasticity, Int. J. Numer. Methods Eng., 7, 1, 297-308 (1973) · Zbl 0264.73113
[9] Kuna, M.; Zwicke, M., A mixed hybrid finite element for three-dimensional elastic crack analysis, Int. J. Fract., 45, 1, 65-79 (1990)
[10] Chen, M. C.; Ping, X. C., A novel hybrid element analysis for piezoelectric-parent material wedges, Comput. Mech., 40, 1, 13-24 (2007) · Zbl 1162.74041
[11] Ping, X. C.; Chen, M. C., A novel hybrid finite element analysis of in-plane singular elastic field around inclusion corners in elastic media, Int. J. Solids Struct., 46, 13, 2527-2538 (2009) · Zbl 1167.74583
[12] Isiet, M.; Mišković, I.; Mišković, S., Review of peridynamic modelling of material failure and damage due to impact, Int. J. Impact Eng., 147, Article 103740 pp. (2021)
[13] Diehl, P.; Lipton, R.; Wick, T.; Tyagi, S., A comparative review of peridynamics and phase-field models for engineering fracture mechanics, Comput. Mech., 69, 1259-1293 (2022) · Zbl 1505.74191
[14] Bui, T. Q.; Hu, X. F., A review of phase-field models, fundamentals and their applications to composite laminates, Eng. Fract. Mech., 8, Article 107705 pp. (2021)
[15] Zhang, P.; Tan, S. Y.; Hu, X. F.; Yao, W. A.; Zhuang, X. Y., A double-phase field model for multiple failures in composites, Compos. Struct., 293, Article 115730 pp. (2022)
[16] Chati, M. K.; Mukherjee, S., The boundary node method for three-dimensional problems in potential theory, Int. J. Numer. Methods Eng., 47, 1523-1547 (2002) · Zbl 0961.65100
[17] Zhang, J. M.; Qin, X. Y.; Han, X.; Li, G. Y., A boundary face method for potential problems in three dimensions, Int. J. Numer. Methods Eng., 80, 320-337 (2009) · Zbl 1176.74212
[18] Fu, Z. J.; Xi, Q.; Gu, Y.; Li, J. P.; Qu, W. Z.; Sun, L. L.; Wei, X.; Wang, F. J.; Lin, J.; Li, W. W.; Xu, W. Z.; Zhang, C. Z., Singular boundary method: A review and computer implementation aspects, Eng. Anal. Bound. Elem., 147, 231-266 (2023) · Zbl 1521.74318
[19] Blandford, G. E.; Ingraffea, A. R.; Liggett, J. A., Two-dimensional stress intensity factor computations using the boundary element method, Int. J. Numer. Methods Eng., 17, 3, 387-404 (1981) · Zbl 0463.73082
[20] Ariza, M. P.; Saez, A.; Dominguez, J., A singular element for three-dimensional fracture mechanics analysis, Eng. Anal. Bound. Elem., 20, 4, 275-285 (1997)
[21] Zhang, J. M.; Dong, Y. Q.; Ju, C. M.; Lin, W. C., A new singular element for evaluating stress intensity factors of V-shaped notches under mixed-mode load, Eng. Anal. Bound. Elem., 93, 161-166 (2018) · Zbl 1403.74263
[22] Gu, Y.; Zhang, C. Z., Novel special crack-tip elements for interface crack analysis by an efficient boundary element method, Eng. Fract. Mech., 239, 11, Article 107302 pp. (2020)
[23] Niu, Z. R.; Cheng, C. Z.; Ye, J. Q.; Recho, N., A new boundary element approach of modeling singular stress fields of plane V-notch problems, Int. J. Solids Struct., 46, 2999-3008 (2009) · Zbl 1167.74590
[24] Cheng, C. Z.; Niu, Z. R.; Recho, N., Analysis of the stress singularity for a bi-material V-notch by the boundary element method, Appl. Math. Modell., 37, 22, 9398-9408 (2013) · Zbl 1449.74100
[25] Greengard, L. F.; Rokhlin, V., A fast algorithm for particle simulations, J. Comput. Phys., 135, 2, 280-292 (1987) · Zbl 0898.70002
[26] Greengard, L. F.; Rokhlin, V., A new version of the fast multipole method for the Laplace equation in three dimensions, Acta Numer., 6, 229-269 (1997) · Zbl 0889.65115
[27] Nishimura, N.; Yoshida, K. I.; Kobayashi, S., A fast multipole boundary integral equation method for crack problems in 3D, Eng. Anal. Bound. Elem., 23, 1, 97-105 (1999) · Zbl 0953.74074
[28] Wang, P. B.; Yao, Z. H., Fast multipole DBEM analysis of fatigue crack growth, Comput. Mech., 38, 3, 223-233 (2006) · Zbl 1162.74047
[29] Guo, Z.; Liu, Y. J.; Ma, H.; Huang, S., A fast multipole boundary element method for modeling 2-D multiple crack problems with constant elements, Eng. Anal. Bound. Elem., 47, 1-9 (2014) · Zbl 1297.74146
[30] Liu, Y. J.; Li, Y. X.; Xie, W., Modeling of multiple crack propagation in 2-D elastic solids by the fast multipole boundary element method, Eng. Fract. Mech., 172, 1-16 (2017)
[31] Liu, Y. J., Fast Multipole Boundary Element Method (2009), Cambridge University Press
[32] Hu, B.; Niu, Z. R.; Li, C.; Hu, Z. J., A fast multipole boundary element method based on higher order elements for analyzing 2-D elastostatic problems, Eng. Anal. Bound. Elem., 130, 2, 417-428 (2021) · Zbl 1521.74294
[33] Williams, M. L., On the stress distribution at the base of a stationary crack, J. Appl. Mech., 24, 109-114 (1957) · Zbl 0077.37902
[34] Niu, Z. R.; Ge, D. L.; Cheng, C. Z.; Ye, J. Q.; Recho, N., Evaluation of the stress singularities of plane V-notches in bonded dissimilar materials, Appl. Math. Modell., 33, 3, 1776-1792 (2009) · Zbl 1168.74314
[35] Johnston, P. R.; Elliott, D., Transformations for evaluating singular boundary element integrals, J. Comput. Appl. Math., 146, 231-251 (2002) · Zbl 1014.65019
[36] Gao, X. W.; Yang, K.; Wang, J., An adaptive element subdivision technique for evaluation of various 2D singular boundary integrals, Eng. Anal. Bound. Elem., 32, 8, 692-696 (2008) · Zbl 1244.65199
[37] Zhang, C.; Fu, Z. J.; Zhang, Y. M., A novel high-order collocation indirect boundary element method based on the Leis formulation for three-dimensional high frequency exterior acoustic problems, Int. J. Numer. Methods Eng., 124, 3, 670-695 (2023) · Zbl 07769179
[38] Matsumto, T.; Tanaka, M.; Obara, R., Computation of stress intensity factors of interface cracks based on interaction energy release rates and BEM sensitivity analysis, Eng. Fract. Mech., 65, 6, 683-702 (2000)
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