Boundary layer effect in BEM with high order geometry elements using transformation

CMES - Computer Modeling in Engineering and Sciences

Volumn 45, Issue 3, 2009, Pages 227-247

  Zhang, Y M ^a   Gu, Y ^a   Chen, J T ^b  

^a SHANDONG UNIVERSITY OF TECHNOLOGY   (China)

^b NATIONAL TAIWAN OCEAN UNIVERSITY   (Taiwan)

Author keywords

BEM; Elasticity problem; High order elements; Nearly singular integrals; Transformation

Indexed keywords

BOUNDARY LAYER EFFECTS; COMPUTATIONAL EFFORT; ELASTICITY PROBLEMS; ENGINEERING PROCESS; GEOMETRICAL DOMAIN; GEOMETRY ELEMENT; HIGH ORDER; HIGH ORDER ELEMENT; NEARLY SINGULAR INTEGRAL; NON-LINEAR TRANSFORMATIONS; NON-LINEARITY; NUMERICAL RESULTS; PRACTICAL PROBLEMS; RAPID VARIATION; SINGULAR KERNEL;

ELASTICITY;

BOUNDARY ELEMENT METHOD;

EID: 76249122916     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (53)

1. Albuquerque, E.L.; Aliabadi, M.H. (2008): A Boundary Element Formulation for Boundary Only Analysis of Thin Shallow Shells. CMES: Computer Modeling in Engineering and Sciences, vol.29, no.2, pp. 63-73.
2. Atluri, S.N. (2004a): The meshless method (MLPG) for domain and BIE discretizations. Forsyth, GA, USA, Tech Science Press.
3. Atluri, S.N. (2005): Methods of computer modeling in engineering and the sciences. Tech Science Press.
4. Atluri, S.N.; Han, Z.D.; Rajendran, A.M. (2004b): A new implementation of the meshless finite volume method through the MLPG "mixed" approach. CMES: Computer Modeling in Engineering and Sciences, vol. 6, no. 6, pp. 491-514.
5. Atluri, S.N.; Liu, H.T.; Han, Z.D. (2006): Meshless local Petrov-Galerkin (MLPG) mixed collocation method for elasticity problems. CMES: Computer Modeling in Engineering and Sciences, vol.14, no.3, pp. 141-152.
6. Brebbia, C.A.; Tells, J.C.F.; Wrobel, L.C. (1984): Boundary Element Techniques. Berlin, Heidelberg, New York, Tokyo: Springer.
7. Cerrolaza, M.; Alarcon, E. (1989): A bi-cubic transformation of the Cauchy principal value integrals in boundary methods. Int J Numer Methods Engng, vol.28, pp. 987-999.
8. Chen, H.B.; Lu, P.; Huang, M.G.; Williams, F.W. (1998): An effective method for finding values on and near boundaries in the elastic BEM. Comput Struct, vol.69(4), pp. 421-431.
9. Chen, J.T. (2000): Recent development of dual BEM in acoustic problems. Comput Methods Appl Mech Eng, vol.188, pp. 833-845.
10. Chen, J.T.; Chen, K.H.; Chen, C.T. (2002): Adaptive boundary element method of time-harmonic exterior acoustics in two dimensions. Comput Methods Appl Mech Eng, vol.191, pp. 3331-3345.
11. Chen, X.L.; Liu, Y.J. (2001): Thermal stress analysis of multi-layer thin films and coatings by an advanced boundary element method. CMES: Computer Modeling in Engineering and Sciences, vol.2(3), pp. 337-349
12. Cruse, T.A. (1974): An improved boundary integral equation method for three dimensional elastic stress analysis. Compt Struct, vol.4, pp. 741-754.
13. Cruse, T.A.; Aithal, R.A. (1993): A new integration algorithm for nearly singular BIE kernels. Int J Numer Methods Eng, vol.36, pp. 237-254.
14. Davies, A.J.; Crann, D.; Kane, S.J.; Lai, C.H. (2007): A Hybrid Laplace Transform/Finite Difference Boundary Element Method for Diffusion Problems. CMES: Computer Modeling in Engineering and Sciences, vol.18, no.2, pp. 79-85.
15. Earlin, L. (1992): Exact Gaussian quadrature methods for near-singular integrals in the boundary element method. Eng Anal Bound Elem, vol.9, pp. 233-245.
16. Earlin, L. (1993): A mapping method for numerical evaluation of two-dimensional integrals with singularity. Compul Mech, vol.12, pp. 19-26.
17. Fratantonio, M.; Rencis, J.J. (2000): Exact boundary element integrations for two-dimensional Laplace equation. Eng Anal Bound Elem, vol.24, pp. 325-342
18. Friedrich, F. (2002): A linear analytical boundary element method for 2D homogeneous potential problems. Comput Geosci, vol.28, pp. 679-692
19. Gao, X.W.; Yang, K.; Wang, J. (2008): An adaptive element subdivision technique for evaluation of various 2D singular boundary integrals. Eng Anal Bound Elem, vol.32, pp. 692-696.
20. Gray, L.J.; Garzon, M.; Mantic, V.E. (2006): Graciani, Galerkin boundary integral analysis for the axisymmetric Laplace equation. Int J Numer Methods Eng, vol.66, pp. 2014-2034.
21. Granados, J.J.; Gallego, G. (2001): Regularization of nearly hypersingular integrals in the boundary element method. Eng Anal Bound Elem, vol.25, pp. 165-184.
22. Guiggiani, M.; Krishnasamy, G.; Rudolphi, T.J.; Rizzo, F.J. (1992): A general algorithm for the numerical solution of hypersingular BEM. J Appl Mech, vol.59, pp. 604-627.
23. Guz, A.N.; Menshykov, O.V.; Zozulya, V.V.; Guz, I.A. (2007): Contact Problem for the Flat Elliptical Crack under Normally Incident ShearWave. CMES: Computer Modeling in Engineering and Sciences, vol.17, no.3, pp. 205-214.
24. Huang, Q.; Cruse, T.A. (1993): Some notes on singular integral techniques in boundary element analysis. Int J Numer Methods Engng, vol.36, pp. 2643-2659.
25. Johnston, P.R. (1999): Application of sigmoidal transformations to weakly singular and near singular boundary element integrals. Int J Numer Meth Eng, vol.45, pp. 1333-1348.
26. Johnston, P.R. (2000): Semi-sigmoidal transformations for evaluating weakly singular boundary element integrals. Int J Numer Meth Eng, vol.47, pp. 1709-1730.
27. Jun, L.; Beer, G.; Meek (1985): Efficient evaluation of integrals of order using Gauss quadrature. Engng Anal, vol.2, pp. 118-123
28. Karlis, G.F.; Tsinopoulos, S.V.; Polyzos, D.; Beskos, D.E. (2008): 2D and 3D Boundary Element nalysis of Mode-I Cracks in Gradient Elasticity. CMES: Computer Modeling in Engineering and Sciences, vol.26, no.3, pp. 189-207.
29. Lachat, J.C.; Watson, J.O. (1976): Effective numerical treatment of boundary integral equation: a formulation for elastostatics. Int J Numer Meth Eng, vol.21, pp. 211-228.
30. Li, J.; Wu, J.M.; Yu, D.H. (2009): Generalized Extrapolation for Computation of Hypersingular Integrals in Boundary Element Methods. CMES: Computer Modeling in Engineering and Sciences, vol.42, no.2, pp. 151-175.
31. Lifeng, M.A.; Alexander, M.; Korsunsky (2004): A note on the Gauss-Jacobi quadrature formulae for singular integral equations of the second kind. Int J Fract, vol.126, pp. 339-405.
32. Liu, C.S.; Chang, C.W.; Chang, J.R. (2008): A New Shooting Method for Solving Boundary Layer Equations in Fluid Mechanics. CMES: Computer Modeling in Engineering and Sciences, vol.32, no.1, pp. 1-15.
33. Liu, Y.J. (1998): Analysis of shell-like structures by the boundary element method based on 3-D elasticity: formulation and verification. Int J Numer Meth Engng, vol.41, pp. 541-558.
34. Luo, J.F.; Liu, Y.J.; Berger, E.J. (1998): Analysis of two-dimensional thin structures (from micro-to nano-scales) using the boundary element method. Comput Mech, vol.22, pp. 404-412.
35. Ma, H.; Kamiya, N. (2002): Distance transformation for the numerical evaluation of near singular boundary integrals with various kernels in boundary element method. Eng Anal Bound Elem, vol.26, pp. 329-339.
36. Mukherjee, S.; Chati, M.K.; Shi, X.L. (2000): Evaluation of nearly singular inte grals in boundary element contour and node methods for three-dimensional linear elasticity. Int J Sol Struct, vol.37, pp. 7633-7654.
37. Niu, Z.R.; Cheng, C.Z.; Zhou, H.L.; Hu, Z.J. (2007): Analytic formulations for calculating nearly singular integrals in two-dimensional BEM. Eng Anal Bound Elem, vol.31, pp. 949-964.
38. Sanz, J.A.; Solis, M.; Domingnez, J. (2007): Hypersingular BEM for Piezoelectric Solids: Formulation and Applications for Fracture Mechanics. CMES: Computer Modeling in Engineering and Sciences, vol.17, no.3, pp. 215-229.
39. Sladek, V.; Sladek, J.; Tanaka, M. (1993): Regularization of hypersingular and nearly singular integrals in the potential theory and elasticity. Int J Numer Methods Eng, vol.36, pp. 16-28.
40. Sladek, V.; Sladek, J.; Tanaka, M. (2000): Optimal transformations of the integration variables in computation of singular integrals in BEM. Int J Numer Methods Eng, vol.47, pp. 1263-1283.
41. Sun, H.C.; Zhang, L.Z.; Xu, Q.; Zhang, Y.M. (1999): Nonsingular Boundary Element Method. Dalian: Dalian University of Technology Press (in Chinese).
42. Tanaka, M.; Matsumoto, T.; Nakamura, M. (1991): Boundary element method. Baifukan Press, Tokyo (in Japanese).
43. Tanaka, M.; Sladek, V.; Sladek, J. (1994): Regularization techniques applied to BEM. Appl Mech Rev, vol.47, pp. 457-499.
44. Telles, J.C.F. (1987): A self-adaptive coordinate transformation for efficient numerical evaluation of general boundary element integral. Int J Numer Meth Eng, vol.24, pp. 959-973.
45. Wang, Y.C.; Li, H.Q.; Cheng, H.B.; Wu, Y. (1994) Calculating the stresses and displacements at arbitrary points with the particular solution field method. Acta Mech Sin, vol.26(2), pp. 222-231.
46. Yoon, S.S.; Heister, S.D. (2000): Analytic solution for fluxes at interior points for 2D Laplace equation. Eng Anal Bound Elem, vol.24, pp. 155-160
47. Young, D.L.; Chen, K.H.; Chen, J.T.; Kao, J.H. (2007): A Modified Method of Fundamental Solutions with Source on the Boundary for Solving Laplace Equations with Circular and Arbitrary Domains. CMES: Computer Modeling in Engineering and Sciences, vol.19, no.3, pp. 197-221.
48. Zhang, Y.M.; Wen, W.D. (2004): A kind of new nonsingular boundary integral equations for elastic plane problems. Acta Mech, vol.36(3), pp. 311-321 (in Chinese).
49. Zhang, Y.M.; Sun, C.L. (2008): A general algorithm for the numerical evaluation of nearly singular boundary integrals in the equivalent non-singular BIES with indirect unknowns. Journal of the Chinese Institute of Engineers, vol.31, pp. 437-447.
50. Zhang, Y.M.; Sun, H.C. (2001): Analytical treatment of boundary integrals in direct boundary element analysis of plane potential and elasticity problems. Appl Math Mech, vol.6, pp. 664-673.
51. Zhang, Y.M.; Sun, H.C. (2000): Theoretic Analysis on Virtual Boundary Element. Chinese J Comp Mech, vol.17, pp. 56-62 (in Chinese).
52. Zhang, X.S.; Zhang, X.X. (2004): Exact integrations of two-dimensional highorder discontinuous boundary element ofelastostatics problems. Eng Anal Bound Elem, vol.28, pp. 725-732.
53. Zhou, H. L.; Niu, Z. R.; Cheng, C. Z. (2008): Analytical integral algorithm applied to boundary layer effect and thin body effect in BEM for anisotropic potential problems. Comp and Struct, vol.86, pp. 1656-1671.