| Citation: |
Zhang Yaoming, Li Xiaochao, Vladimir Sladek, Jan Sladek. A GENERAL ALGORITHM FOR CALCULATING NEARLY SINGULAR INTEGRALS OVER HIGH-ORDER ELEMENTS IN 3D BEM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(6): 908-918. DOI: 10.6052/0459-1879-13-057
|
|
Tanaka M, Sladek V, Sladek J. Regularization techniques applied to boundary element methods. Applied Mechanics Reviews, 1994, 47: 457-499
|
|
Chen JT, Hong HK. Review of dual boundary element methods with emphasis on hypersingular integrals and divergent series. Applied Mechanics Reviews, 1999, 52(1): 17-33
|
|
Liu YJ. On the simple solution and non-singular nature of the BIE/BEM-a review and some new results. Engng Anal Bound Elem, 2000, 24: 286-292
|
|
Gao XW. An effective method for numerical evaluation of general 2D and 3D high order singular boundary integrals. Comput Methods Appl Mech Engrg, 2010, 199: 2856-2864
|
|
Zhang YM, Sladek V, Sladek J, et al. A new boundary integral equation formulation for plane orthotropic elastic media. Applied Mathematical Modelling, 2012, 36: 4862-4875
|
|
Sladek V, Sladek J, Tanaka M. Regularization of hypersingular and nearly singular integrals in the potential theory and elasticity. Int J Numer Meth. Engng, 1993, 36(10): 1609-1628
|
|
Chen HB, Lu P, Schnack E. Regularized algorithms for the calculation of values on and near boundaries in 2D elastic BEM. Engng Anal Bound Elem, 2001, 25(10): 851-876
|
|
Gao XW, Yang K, Wang J. An adaptive element subdivision technique for evaluation of various 2D singular boundary integrals. Engng Anal Bound Elem, 2008, 32: 692-696
|
|
Zhang XS, Zhang XX. Exact integrations of two-dimensional high-order discontinuous boundary element of elastostatics problems. Engng Anal Bound Elem, 2003, 28(7): 725-732
|
|
Niu ZR, Wendland WL, Wang XX, et al. A semi-analytical algorithm for the evaluation of the nearly singular integrals in three-dimensional boundary element methods. Comput Methods Appl Mech Engrg, 2005, 194: 1057-1074
|
|
Mukerjee S, Chati MK, Shi XL. Evaluation of nearly singular integrals in boundary element contour and node methods for three-dimensional linear elasticity. Int J Solids Struct, 2000, 37(51): 7633-7654
|
|
Liu YJ. Analysis of shell-like structures by the boundary element method based on 3-D elasticity, formulation and verification. Int J Numer Meth Engng, 1998, 41(3): 541-558 3.0.CO;2-K">
|
|
Milroy J, Hinduja S, Davey K. The elastostatic three-dimensional boundary element method analytical integration for linear isoparametric triangular elements, Appl Math Model, 1997, 21: 763-782
|
|
Nintcheu Fata S. Semi-analytic treatment of nearly-singular Galerkin surface integrals. Applied Numerical Mathematics, 2010, 60: 974-993
|
|
Zhang YM, Gu Y, Chen JT. Stress analysis for multilayered coating systems using semi-analytical BEM with geometric non-linearities. Computational Mechanics, 2011, 47: 493-504
|
|
张耀明, 孙翠莲, 谷岩.边界积分方程中近奇异积分计算的一种变量替换法, 力学学报, 2008, 40(2): 207-214 (Zhang Yaoming, Sun Cuilian, Gu Yan. The evaluation of nearly singular integrals in boundary integral equations with variable transformation. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(2): 207-214 (in Chinese))
|
|
Telles JCF. A self-adaptive coordinate transformation for efficient numerical evaluation of general boundary element integral. Int J Numer Meth Engng, 1987, 24: 959-973
|
|
Johnston PR. Application of Sigmoidal transformations to weakly singular and near singular boundary element integrals. Int J Numer Meth Engng, 1999, 45(10): 1333-1348 3.0.CO;2-Q">
|
|
Huang Q, Cruse TA. Some notes on singular integral techniques in boundary element analysis. Int J Numer Meth Engng, 1993, 36(15): 2643-2659
|
|
Ma H, Kamiya N. Distance transformation for the numerical evaluation of near singular boundary integrals with various kernels in boundary element method. Engng Anal Bound Elem , 2002, 26(4): 329-339
|
|
Qin XY, Zhang JM, Xie GZ, et al. A general algorithm for the numerical evaluation of nearly singular integrals on 3D boundary element. Journal of Computational and Applied Mathematics, 2011, 235: 4174-4186
|
|
Peter R. Johnston1, David Elliott. A sinh transformation for evaluating nearly singular boundary element integrals. Int J Numer Meth Engng, 2005, 62: 564-578
|
|
Letizia S. On the computation of nearly singular integrals in 3D BEM collocation. Int J Numer Meth Engng, 2008, 74: 1733-1770
|
|
Johnston BM, Johnston PR, Elliott D. A new method for the numerical evaluation of nearly singular integrals on triangular elements in the 3D boundary element method. Journal of Computational and Applied Mathematics, 2013, 245:148-161.
|
|
Zhang YM, Gu Y, Chen JT. Boundary layer effect in BEM with high order geometry elements using transformation. Computer Modeling in Engineering and Sciences, 2009, 45(3):227-247.
|
|
Zhang YM, Gu Y, Chen JT. Boundary element analysis of the thermal behaviour in thin-coated cutting tools. Engng. Anal. Bound. Elem., 2010; 34(9):775-784.
|
|
Zhang YM, Qu WZ, Chen JT. BEM analysis of thin structures for thermoelastic problems. Engng Anal Bound Elem, 2013, 37: 441-452
|
|
Gao XW, Davies TG. Adaptive algorithm in elasto-plastic boundary element analysis. Journal of the Chinese Institute of Engineers, 2000, 23(3):349-356
|
|
Chati MK, Mukherjee S, Mukherjee YX. The boundary node method for three-dimensional linear elasticity . Int J Numer Meth Engng, 1999, 46: 1163-1184 3.0.CO;2-Y">
|
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