Analytical integral algorithm in the BEM for orthotropic potential problems of thin bodies

Engineering Analysis with Boundary Elements

Volumn 31, Issue 9, 2007, Pages 739-748

  Zhou, Huanlin ^a,b   Niu, Zhongrong ^a   Cheng, Changzheng ^a   Guan, Zhongwei ^b  

^a HEFEI UNIVERSITY OF TECHNOLOGY   (China)

^b UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

Analytical integral; Bem; Nearly singular integrals; Orthotropic potential problem; Thin body

Indexed keywords

ALGORITHMS; INTEGRAL EQUATIONS; INTEGRATION; INTERPOLATION; NUMERICAL METHODS; PROBLEM SOLVING;

BOUNDARY NODES; INTEGRAL ALGORITHMS; NEARLY SINGULAR INTEGRALS; ORTHOTROPIC POTENTIAL PROBLEMS;

BOUNDARY ELEMENT METHOD;

EID: 34547452670     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2007.01.007     Document Type: Article

References (35)

1. Brebbia C.A., Telles J.C., and Wrobel L.C. Boundary element techniques (1984), Springer, Berlin, Heidelberg
2. Tanaka M., Sladek V., and Sladek J. Regularization techniques applied to BEM. Appl Mech Rev 47 10 (1994) 457-499
3. In: Sladek V., and Sladek J. (Eds). Singular integrals in boundary element methods (1998), Computational Mechanics Publications, Southampton
4. Gray LJ. Evaluation of singular and hypersingular Galerkin integrals: direct limits and symbolic computation. In Sladek V, Sladek J, editors. Singular integrals in boundary element methods. Southampton: Computational Mechanics Publications; 1998. p. 33-84 [chapter 2].
5. Gray L.J., Garzon M., Mantic V., and Graciani E. Galerkin boundary integral analysis for the axisymmetric Laplace equation. Int J Numer Methods Eng 66 (2006) 2014-2034
6. Chen H.B., Lu P., Huang M.G., and Williams F.W. An effective method for finding values on and near boundaries in the elastic BEM. Comput Struct 69 4 (1998) 421-431
7. Ma H., and Kamiya N. Domain supplemental approach to avoid boundary layer effect of BEM in elasticity. Eng Anal Bound Elem 23 (1999) 281-284
8. Ma H., and Kamiya N. A general algorithm for accurate computation of field variables and its derivatives near the boundary in BEM. Eng Anal Bound Elem 25 (2001) 833-841
9. Ma H., and Kamiya N. Distance transformation for the numerical evaluation of near singular boundary integrals with various kernels in boundary element method. Eng Anal Bound Elem 26 (2002) 329-339
10. Ma H., and 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 (2002) 277-288
11. Sladak V., Sladek J., and Tanaka M. Optimal transformations of the integration variables in computation of singular integrals in BEM. Int J Numer Methods Eng 47 (2000) 1263-1283
12. Zhang X.S., and Zhang X.X. Exact integration in the boundary element method for two-dimensional elastostatic problems. Eng Anal Bound Elem 27 (2003) 987-997
13. Zhang X.S., and Zhang X.X. Exact integrations of two-dimensional high-order discontinuous boundary elements of elastostatic problems. Eng Anal Bound Elem 28 (2004) 725-732
14. Zhang X.S., and Zhang X.X. Exact integration for stress evaluation in the boundary element analysis of two-dimensional elastostatics. Eng Anal Bound Elem 28 (2004) 997-1004
15. Niu Z.R., Wang X.X., and Zhou H.L. A general algorithm for calculating the quantities at interior points close to the boundary by the BEM. Acta Mech Sin 33 2 (2001) 275-283 [in Chinese]
16. Niu Z.R., Wang X.X., and Zhou H.L. A non-singular algorithm for the evaluation of the nearly singular integrals in boundary element methods. Chin J Appl Mech 18 4 (2001) 1-8 [in Chinese]
17. Zhou H.L., Niu Z.R., and Wang X.X. Regularization of nearly singular integrals in the BEM of potential problems. Appl Math Mech 24 10 (2003) 1208-1214
18. Niu Z.R., Wendland W.L., Wang X.X., and Zhou H.L. A semi-analytical algorithm for the evaluation of the nearly singular integrals in three-dimensional boundary element methods. Comput Methods Appl Mech Eng 194 (2005) 1057-1074
19. Zhou H.L., Niu Z.R., and Wang X.X. Regularization of nearly singular integrals in the boundary element method for 3-D potential problems. Chin J Comput Phys 22 6 (2005) 501-506 [in Chinese]
20. Niu Z.R., Wang X.X., Zhou H.L., and Zhang C.L. A novel boundary integral equation method for linear elasticity-natural boundary integral equation. Acta Mech Solida Sin 22 2 (2001) 111-119
21. Niu Z.R., and Zhou H.L. The natural boundary integral equation in potential problems and regularization of the hypersingular integral. Comput Struct 82 (2004) 315-323
22. 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 (1998) 541-558
23. Luo J.F., Liu Y.J., and Berger E.J. Analysis of two-dimensional thin structures (from micro- to nano-scales) using the boundary element method. Comput Mech 22 (1998) 404-412
24. Luo J.F., Liu Y.J., and Berger E.J. Interfacial stress analysis for multi-coating systems using an advanced boundary element method. Comput Mech 24 (2000) 448-455
25. Chen X.L., and Liu Y.J. Thermal stress analysis of multi-layer thin films and coatings by an advanced boundary element method. CMES 2 (2001) 337-349
26. Liu Y.J., and Fan H. On the conventional boundary integral equation formulation for piezoelectric solids with defects or of thin shapes. Eng Anal Bound Elem 25 (2001) 77-91
27. Liu Y.J., and Fan H. Analysis of thin piezoelectric solids by the boundary element method. Comput Methods Appl Eng 191 (2002) 2297-2315
28. Zhou HL. Study on boundary layer effect and thin body effect in the BEM. PhD dissertation, Hefei, University of Science and Technology of China; 2003 [in Chinese].
29. Fratantonio M., and Rencis J.J. Exact boundary element integrations for two-dimensional Laplace equation. Eng Anal Bound Elem 24 (2000) 325-342
30. Friedrich J. A linear analytical boundary element method (BEM) for 2D homogeneous potential problems. Comput Geosciences 28 (2002) 679-692
31. Mera N.S., Elliott L., Ingham D.B., and Lesnic D. A comparison of boundary element method formulations for steady state anisotropic heat conduction problems. Eng Anal Bound Elem 25 (2001) 115-128
32. Padhi G.S., Shenoi R.A., Moy S.S.J., and McCarthy M.A. Analytic integration of kernel shape function product integrals in the boundary element method. Comput Struct 79 (2001) 1325-1333
33. Milroy J., Hinduja S., and Davey K. The elastostatic three-dimensional boundary element method analytical integration for linear isoparametric triangular elements. Appl Math Model 21 (1997) 763-782
34. Mukherjee S. CPV and HFP integrals and their applications in the boundary element method. Int J Solids Struct 37 (2000) 6623-6634
35. Mukherjee S., Chati M.K., and Shi X.L. Evaluation of nearly singular integrals in boundary element contour and node methods for three-dimensional linear elasticity. Int J Solids Struct 37 (2000) 7633-7654