An extended boundary node method for modeling normal derivative discontinuities in potential theory across edges and corners

Engineering Analysis with Boundary Elements

Volumn 28, Issue 9, 2004, Pages 1099-1110

  Telukunta, Srinivas ^a   Mukherjee, Subrata ^b  

^a Cornell University   (United States)

^b Department of Obstetrics Gynecology   (United States)

Author keywords

Boundary element method; Boundary node method; Integral equations; Meshfree; Potential theory

Indexed keywords

BOUNDARY VALUE PROBLEMS; ELASTICITY; FINITE ELEMENT METHOD; GALERKIN METHODS; INTEGRAL EQUATIONS; LEAST SQUARES APPROXIMATIONS;

BOUNDARY NODE METHOD (BNM); MESHFREE; POTENTIAL THEORY;

BOUNDARY ELEMENT METHOD;

EID: 3142749246     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2004.01.007     Document Type: Article

References (37)

1. Lancaster P., Salkauskas K. Curve and surface fitting - an introduction. 1990;Academic Press, London.
2. Nayroles B., Touzot G., Villon P. Generalizing the finite element method: diffuse approximation and diffuse elements. Comput Mech. 10:1992;307-318.
3. Belytschko T., Krongauz Y., Organ D., Fleming M., Krysl P. Meshless methods: an overview and recent developments. Comput Meth Appl Mech Engng. 139:1996;3-47.
4. Liu W.K., Chen Y., Jun S., Belytschko T., Pan C., Uras R.A., Chang C.T. Overview and applications of the reproducing kernel particle methods. Arch Comput Meth Engng. 3:1996;3-80.
5. Oden J.T., Duarte C.A.M., Zienkiewicz O.C. A new cloud based hp finite element method. Comput Meth Appl Mech Engng. 153:1998;117-126.
6. Atluri S.N., Shen S. The meshless local Petrov-Galerkin (MLPG) method. 2002;Tech Science Press, Encino, CA.
7. Sukumar N., Moran B., Belytschko T. The natural element method. Int J Numer Meth Engng. 43:1998;839-887.
8. Sukumar N., Moran B., Semenov A.Y., Belytschko T. Natural neighbour Galerkin methods. Int J Numer Meth Engng. 50:2001;1-27.
9. Strouboulis T., Babuška I., Copps K. The design and analysis of the generalized finite element method. Comput Meth Appl Mech Engng. 181:2000;43-69.
10. Dolbow J.E., Möes N., Belytschko T. An extended finite element method for modeling crackgrowth with frictional contact. Comput Meth Appl Mech Engng. 190:2001;6825-6846.
11. Bathe K.J., De S. The method of finite spheres with improved numerical integration. Comput Struct. 79:2001;2183-2196.
12. Aluru N.R., Li G. Finite cloud method: a true meshless technique based on a fixed reproducing kernel approximation. Int J Numer Meth Engng. 50:2001;2373-2410.
13. Liu G.R. Mesh-free methods: moving beyond the finite element method. 2002;CRC Press, Boca Raton, FL.
14. Mukherjee S. Boundary element methods in creep and fracture. 1982;Applied Science Publishers, London.
15. Banerjee P.K. The boundary element methods in engineering. 1994;McGraw-Hill, Maidenhead.
16. Chandra A., Mukherjee S. Boundary element methods in Manufacturing. 1997;Oxford University Press, New York.
17. Bonnet M. Boundary integral equation methods for solids and fluids. 1999;Wiley, Chichester, UK.
18. Mukherjee Y.X., Mukherjee S. The boundary node method for potential problems. Int J Numer Meth Engng. 40:1997;797-815.
19. Kothnur V., Mukherjee S., Mukherjee Y.X. Two-dimensional linear elasticity by the boundary node method. Int J Solid Struct. 36:1999;1129-1147.
20. Chati M.K., Mukherjee S. The boundary node method for three-dimensional problems in potential theory. Int J Numer Meth Engng. 47:2000;1523-1547.
21. Chati M.K., Mukherjee S., Mukherjee Y.X. The boundary node method for three-dimensional linear elasticity. Int J Numer Meth Engng. 46:1999;1163-1184.
22. Chati M.K., Paulino G.H., Mukherjee S. The meshless standard and hypersingular boundary node methods - applications to error estimation and adaptivity in three-dimensional problems. Int J Numer Meth Engng. 50:2001;2233-2269.
23. Chati M.K., Mukherjee S., Paulino G.H. The meshless hypersingular boundary node method for three-dimensional potential theory and linear elasticity problems. Engng Anal Bound Elem. 25:2001;639-653.
24. Gowrishankar R., Mukherjee S. The 'pure' boundary node method for potential theory. Commun Numer Meth Engng. 18:2002;411-427.
25. Zhu T., Zhang J.D., Atluri S.N. A local boundary integral equation (LBIE) method in computational mechanics, and a meshless discretization approach. Comput Mech. 21:1998;223-235.
26. Sladek J., Sladek V., Atluri S.N. Local boundary integral equation (LBIE) method for solving problems of elasticity with nonhomogeneous material properties. Comput Mech. 24:2000;456-462.
27. Chen W., Tanaka M. A meshless, integration-free, boundary-only RBF technique. Comput Math Appl. 43:2002;379-391.
28. Li G., Aluru N.R. Boundary cloud method: a combined scattered point/boundary integral approach for boundary-only analysis. Comput Meth Appl Mech Engng. 191:2002;2337-2370.
29. Li G., Aluru N.R. A boundary cloud method with a cloud-by-cloud polynomial basis. Engng Anal Bound Elem. 27:2003;57-71.
30. Belytschko T., Lu Y.Y., Gu L. Element-free Galerkin methods. Int J Numer Meth Engng. 37:1994;229-256.
31. Mukherjee S., Mukherjee Y.X. Boundary methods - elements contours and nodes. 2004;Marcel Dekker, New York. in press.
32. Gu Y.T., Liu G.R. A boundary point interpolation method for stress analysis of solids. Comput Mech. 28:2002;47-54.
33. Gu Y.T., Liu G.R. A radial basis boundary point interpolation method for stress analysis of solids. Struct Engng Mech. 15:2003;535-550.
34. Gu Y.T., Liu G.R. Hybrid boundary point interpolation methods and their coupling with the element free Galerkin method. Engng Anal Bound Elem. 27:2003;905-917.
35. Liu G.R., Gu Y.T. Coupling of element free Galerkin and hybrid boundary element methods using modified variational formulation. Comput Mech. 26:2000;166-173.
36. Liu G.R., Gu Y.T. Meshless local Petrov-Galerkin (MLPG) method in combination with finite element and boundary element approaches. Comput Mech. 26:2000;536-546.
37. Gu Y.T., Liu G.R. A coupled element free Galerkin/boundary element method for stress analysis of two-dimensional solids. Comput Meth Appl Mech Engng. 190:2002;4405-4419.