×

A new implementation of BEM by an expanding element interpolation method. (English) Zbl 1403.74005

Summary: A new implementation of boundary element method (BEM) by an expanding element interpolation method is presented in this paper. The expanding element is achieved by collocating virtual nodes along the perimeter of the traditional discontinuous element. With the virtual nodes, both continuous and discontinuous fields on the domain boundary can be accurately approximated, and the interpolation accuracy increases by two orders compared with the original discontinuous element. The boundary integral equations are built up for the inner nodes of the traditional discontinuous elements, only (taking these nodes as source points), while the virtual nodes are used for connecting the shape functions at the source points, thus the size of the final system of linear equations will not increase. The expanding element inherits the advantages of both the continuous and discontinuous elements while overcomes their disadvantages. Successful numerical examples with different boundary conditions have demonstrated that our new implementation is very encouraging and promising.

MSC:

74-04 Software, source code, etc. for problems pertaining to mechanics of deformable solids
74S15 Boundary element methods applied to problems in solid mechanics
65N38 Boundary element methods for boundary value problems involving PDEs

Software:

neBEM
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Brebbia, C. A.; Telles, J. C.F.; Wrobel, L. C., Boundary element techniques: theory and applications in engineering, 5, (1984), Springer-Verlag Berlin · Zbl 0556.73086
[2] Cheng, A. H.D.; Cheng, D. T., Heritage and early history of the boundary element method, Eng Anal Bound Elem, 29, 268-302, (2005) · Zbl 1182.65005
[3] Yao, Z. H., A new type of high-accuracy BEM and local stress analysis of real beam, plate and shell structures, Eng Anal Bound Elem, 65, 1-17, (2016) · Zbl 1403.74260
[4] 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
[5] Zhou, F. L.; Zhang, J. M.; Sheng, X. M.; Li, G. Y., A dual reciprocity boundary face method for 3D non-homogeneous elasticity problems, Eng Anal Bound Elem, 36, 1301-1310, (2012) · Zbl 1351.74088
[6] Zhuang, C.; Zhang, J. M.; Qin, X. Y.; Zhou, F. L.; Li, G. Y., Integration of subdivision method into boundary element analysis, Int J Comput Methods, 09, 367-374, (2012)
[7] Xie, G. Z.; Zhang, J. M.; Huang, C.; Lu, C. J.; Li, G. Y., A direct traction boundary integral equation method for three-dimension crack problems in infinite and finite domains, Comput Mech, 53, 575-586, (2014) · Zbl 1398.74445
[8] Zhang, J. M.; Huang, C.; Lu, C. J.; Han, L.; Wang, P.; Li, G. Y., Automatic thermal analysis of gravity dams with fast boundary face method, Eng Anal Bound Elem, 41, 111-121, (2014)
[9] Dong, Y. Q.; Zhang, J. M.; Xie, G. Z.; Lu, C. J.; Han, L.; Wang, P., A general algorithm for the numerical evaluation of domain integrals in 3D boundary element method for transient heat conduction, Eng Anal Bound Elem, 51, 30-36, (2015) · Zbl 1403.80019
[10] Chen, J. T.; Hong, H. K., Review of dual boundary element methods with emphasis on hypersingular integrals and divergent series, Appl Mech Rev, 52, 17-33, (1999)
[11] Liu, Y. J., Analysis of shell-like structures by the boundary element method based on 3-D elasticity: formulation and verification, Int J Numer Methods Eng, 41, 541-558, (1998) · Zbl 0910.73068
[12] Johnston, B. M.; Johnston, P. R.; Elliott, D., A new method for the numerical evaluation of nearly singular integrals on triangular elements in the 3D boundary element method, J Comput Appl Math, 245, 148-161, (2013) · Zbl 1262.65043
[13] Maestre, J.; Cuesta, I.; Pallares, J., An unsteady 3D isogeometrical boundary element analysis applied to nonlinear gravity waves, Comput Methods Appl Mech Eng, (2016), [Accepted]
[14] Rosen, D.; Cormack, D. E., On corner analysis in the BEM by the continuation approach, Eng Anal Bound Elem, 16, 53-63, (1995)
[15] Shen, J.; Sterz, O., A mixed Galerkin and collocation approach for treating edge and corner problems in the boundary element method, Magn IEEE Trans, 34, 3296-3299, (1998)
[16] Mukhopadhyay, S.; Majumdar, N., A study of three-dimensional edge and corner problems using the nebem solver, Eng Anal Bound Elem, 33, 105-119, (2009) · Zbl 1244.78025
[17] Guiggiani, M.; Krishnasamy, G.; Rudolphi, T. J.; Rizzo, F. J., A general algorithm for the numerical solution of hypersingular boundary integral equations, J Appl Mech, 59, 604-614, (1992) · Zbl 0765.73072
[18] Cisilino, A., Linear and nonlinear crack growth using boundary elements, (2000), WIT Press Southampton · Zbl 1007.74004
[19] Manolis, G. D.; Banerjee, P. K., Conforming versus non-conforming boundary elements in three-dimensional elastostatics, Int J Numer Methods Eng, 23, 1885-1904, (1986) · Zbl 0597.73084
[20] Parreira, P., On the accuracy of continuous and discontinuous boundary elements, Eng Anal, 5, 205-211, (1988)
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.