A singular element based on dual interpolation BFM for V-shaped notches. (English) Zbl 1481.65248
Summary: A singular element based on dual interpolation boundary face method (DiBFM) is presented for solving V-shaped notch problems in this paper. The stress field around sharp notches is singular, and the singularity orders vary with the notch angle. Thus an element with usual shape functions or traditional singular element cannot lead to high accurate results. To accurately model the distribution of displacement around the notch tip, a new displacement singular element based on DiBFM is proposed. The new element takes into account the variable singularity orders at the notch tip. The dual interpolation method which combines conventional polynomial element interpolation and moving least-squares approximation can provide much higher accuracy than traditional interpolation method. With the proposed singular element based on DiBFM, more accurate displacement results in the vicinity of the notch tip can be evaluated, thus more accurate stress intensity factor (SIF) of the V-shaped notches can be obtained. Numerical examples have demonstrated the validity and accuracy of our method.
MSC:
| 65N38 | Boundary element methods for boundary value problems involving PDEs |
Keywords:
V-shaped notch; singular element; stress intensity factor (SIF); dual interpolation; boundary face method (BFM)References:
| [1] | Zhang, J. M.; Lin, W. C.; Dong, Y. Q., A double-layer interpolation method for implementation of BEM analysis of problems in potential theory, Appl. Math. Model., 51, 250-269 (2017) · Zbl 1480.65359 |
| [2] | Xie, G. Z.; Zhang, J. M.; Dong, Y. Q., An improved exponential transformation for nearly singular boundary element integrals in elasticity problems, Int. J. Solids Struct., 51, 6, 1322-1329 (2014) |
| [3] | Dong, Y. Q.; Zhang, J. M.; Xie, G. Z., A general algorithm for evaluating domain integrals in 2D boundary element method for transient heat conduction, Int. J. Comput. Methods, 12, 2, Article 1550010 pp. (2015), . 13 pages · Zbl 1359.65185 |
| [4] | Li, Y.; Zhang, J. M.; Xie, G. Z., Time-domain BEM analysis for three-dimensional elastodynamic problems with initial conditions, CMES-Comput. Model. Eng. Sci., 101, 3, 187-206 (2014) · Zbl 1356.74233 |
| [5] | Zhang, J. M.; Lu, C. J.; Li, Y., A domain renumbering algorithm for multi-domain boundary face method, Eng. Anal. Bound. Elem., 44, 19-27 (2014) · Zbl 1297.65187 |
| [6] | Huang, C.; Zhang, J. M.; Qin, X. Y., Stress analysis of solids with open-ended tubular holes by BFM, Eng. Anal. Bound. Elem., 36, 1908-1916 (2012) · Zbl 1351.74109 |
| [7] | Qin, X. Y.; Zhang, J. M.; Li, G. Y., An element implementation of the boundary face method for 3D potential problems, Eng. Anal. Bound. Elem., 34, 934-943 (2010) · Zbl 1244.74182 |
| [8] | Li, J. P.; Chen, W., A modified singular boundary method for three-dimensional high frequency acoustic wave problems, Appl. Math. Model., 54, 189-201 (2018) · Zbl 1480.74151 |
| [9] | Muñoz-Reja, M. M.; Buroni, F. C.; Sáez, A., 3D explicit-BEM fracture analysis for materials with anisotropic multifield coupling, Appl. Math. Model., 40, 4, 2897-2912 (2016) · Zbl 1452.74011 |
| [10] | Zhao, P.; Qin, T. Y.; Zhang, L. N., A regularized time-domain BIEM for transient elastodynamic crack analysis in piezoelectric solids, Eng. Anal. Bound. Elem., 56, 145-153 (2015) · Zbl 1403.74267 |
| [11] | Liu, Y. J.; Fan, H., Analysis of the thin piezoelectric solids by the boundary element method, Comput. Methods Appl. Mech. Eng., 191, 2297-2315 (2002) · Zbl 1131.74342 |
| [12] | Ma, H.; Kamiya, N., A general algorithm for the numerical evaluation of nearly singular boundary integrals of various orders for two- and three-dimensional elasticity, Comput. Mech., 29, 4, 277-288 (2002) · Zbl 1128.74343 |
| [13] | Dong, C. Y.; Xie, Z. C.; Yao, Z. H., Some numerical solution methods of hypersingular integrals in BIE, Adv. Mech., 25, 3, 424-429 (1995) · Zbl 0850.73344 |
| [14] | Qin, Q. H.; Huang, Y. Y., BEM of postbuckling analysis of thin plates, Appl. Math. Model., 14, 10, 544-548 (1990) · Zbl 0709.73087 |
| [15] | Rzasnicki, W.; Mendelson, A., Application of boundary integral method to elastoplastic analysis of V-notched beams, Int. J. Fract., 11, 2, 329-342 (1975) |
| [16] | Portela, A.; Aliabadi, M. H.; Rooke, D. P., Efficient boundary element analysis of sharp notched plates, Int. J. Numer. Methods Eng., 32, 3, 445-470 (1991) · Zbl 0758.73061 |
| [17] | Niu, Z. R.; Cheng, C. Z.; Ye, J. Q., A new boundary element approach of modeling singular stress fields of plane V-notch problems, Int. J. Solids Struct., 46, 16, 2999-3008 (2009) · Zbl 1167.74590 |
| [18] | Cheng, C. Z.; Ge, S. Y.; Yao, S. L., Singularity analysis for a V-notch with angularly inhomogeneous elastic properties, Int. J. Solids Struct., 78, 138-148 (2016) |
| [19] | Zhang, J. M.; Dong, Y. Q.; Ju, C. M., 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 |
| [20] | Zhang, J. M.; Han, L.; Lin, W. C., A new implementation of BEM by an expanding element interpolation method, Eng. Anal. Bound. Elem., 78, 1-7 (2017) · Zbl 1403.74005 |
| [21] | Zhang, J. M.; Zhong, Y. D.; Dong, Y. Q., Expanding element interpolation method for analysis of thin-walled structures, Eng. Anal. Bound. Elem., 86, 82-88 (2018) · Zbl 1403.65242 |
| [22] | Giannopoulos, G. I.; Anifantis, N. K., Thermal fracture interference: a two-dimensional boundary element approach, Int. J. Fract., 132, 4, 351-369 (2005) · Zbl 1196.74271 |
| [23] | Katsareas, D. E.; Giannopoulos, G. I.; Anifantis, N. K., A comparative study on the failure resistance of thermal barrier coatings, Comput. Struct., 84, 29-30, 1958-1964 (2006) |
| [24] | Kuang Z.B., Ma F. S. Crack tip fields (in Chinese). Xi’an: Xi’an Jiaotong University Press; 2002.; Kuang Z.B., Ma F. S. Crack tip fields (in Chinese). Xi’an: Xi’an Jiaotong University Press; 2002. |
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.
